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(a) Complete the table of values for y = 3 x − 2 x −3 −2 −1 0 1 2 3 y −11 −5 7 (2) (b) On the grid below, draw the graph of y = 3 x − 2 O x y 12 10 8 6 4 2 –2 –4 –6 –8 –10 –12 –3 –2 –1 1 2 3 (2) (Total 4 marks) 6 A straight line has equation y = 5 – 3x (a) Write down the gradient of the lineEquation of a line is y = 2 x a) A is a point on the line If the x coordinate of A is − 2, find its y coordinate b) Verify whether a circle of(a) Complete the table of values for y = 2x 3 (b) On the grid, draw the graph of y = 2x 3 (c) Use your graph to find (i) the value of y when x = 15 (ii) the value of x when y = 6 Example 3 On the grid, draw the graph of y = 3x 2 for the values of x from 1 to 3 Example 4 On the grid, draw the graph of y = 3 2x for the values of x from 2 to 4 Example 5

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X y=2 straight line graph-Variables x and y are such that, when y2 is plotted against sec x, a straight line graph passing through the points (24, 16) and (13, 38) is obtained (i) Express y2 in terms of sec x 3 (ii) Hence find the exact value of cos x when y = 2 2 1 O y –– x2 x3 ×Excel makes graphing easy Line graphs are one of the standard graph options in Excel, along with bar graphs and stacked bar graphsWhile bar graphs may be best for showing proportions and other data points, line graphs are ideal for tracking trends and predicting the results of data in yettoberecorded time periods

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This lesson on interpreting straight line graphs is available here Equation of a line using coordinate pairs The starter recaps the learning in the previous lesson on using graphs to solve equations by interpreting the x and y values of a line By adding the x and y values together students can see the equation of the line is x y = 5Revise straight line graphs Model straight line graphs Lesson From Grade 9 y = mx c • Straight line graph • Linear Function m is the gradient c is the y–intercept To draw the graph we simply need two points Example Sketch y = 2x − 1 Start with c c = − 1 m = _2 1 Plot the gradient Properties of straight line graphs ax by c = 0The effect of a negative value of b;

To find the yintercept Let x=0 in the equation, then solve for y The yintercept is ( 0, –2 ) Now we can plot the two points on the xy axis and connect them using a straight edge ruler to show the graph of the line Example 2 Graph the equation of the line using its intercepts This equation of the line is in the SlopeIntercept FormWe can draw a straight line graph of the form y = m x c using the gradient ( m) and the y intercept ( c ) We calculate the y intercept by letting x = 0 This gives us one point ( 0;Consider the straight line with equation y = 2x1 This equation is in a slightly different form from those we have seen earlier To draw a sketch of the line, we must calculate some values y = 2x1 x y 0 1 1 3 2 5 x y y = 2x 1 Notice that when x = 0 the value of y is 1 So this line cuts the yaxis at y = 1 What about the line y = 2x4?

I understand this is probably a duplicate question, but the answers on said duplicates don't make sense to me or don't seem to work for me I'm being asked to find the point of tangency and the equation for the tangent lineReview 1 The line segment AB has coordinates A(4,9) and B(13, 18) What is the length of the line AB?Grey College 2 DAY 24 1 Straight line graphs y = m x c m = gradient = ∆ ∆ = 2− 1 2− 1 c = y – intercept 1) axis m line has an increasing gradient 2) axis m – line has a decreasing gradient Draw the straight line by using the table method If the c – value of the straight line is 0,

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The xintercept of a graph is that value of x where the graph crosses the xaxis The yintercept is the value of y where it crosses the yaxis To find the xintercept, we have to find the value of x where y = 0 because at every point on the xaxis, y = 0 Example 1 Calculate the value of x when y = 0, that is, find the xintercept of y = 2x 10 Solution On putting y = 0, we have to solve theWhat we can see from a line graph, but would not be so obvious from the table of results, is whether the line is straight or curved So, we could talk of a 'straight line graph' for which 'as x increases, y steadily increases' (Figure 73a) or for which 'as xHow to create a horizontal line

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Straight line graphs DAC Quiz 1) This graph has a gradient of a) 0 b) 1 c) 2 d) 3 2) This line has intercept a) 1 b) 2 c) 3 d) 4 3) This is the graph of a) y = 1 b) y = 3 c) x = 1 d) x = 3 4) This graph has a gradient of a) 05 b) 1 c) 2 d) 3 5) This is the graph ofView my channel http//wwwyoutubecom/jayates79Answer (1 of 76) This equation is in what we call "pointslope form", yb=m(xa), where (a,b) is a point on the line and m is its slope Which means that by looking at the equation we can see that it passes through the point (3,2) and that it has a slope of 2 Begin by location the point (3,2)

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The effect of a negative value of m;×(7, 1) (3, 9) ––The variables x and y are related so that, when y x2See a solution process below To graph a linear equation we need to find two points on the line and then draw a straight line through them Point 1 Let x = 0 0 y = 2 y = 2 or (0, 2) Point 2 Let y = 0 x 0 = 2 x = 2 or (2, 0) Graph graph{(xy

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Graph y=2x3 y = 2x − 3 y = 2 x 3 Use the slopeintercept form to find the slope and yintercept Tap for more steps The slopeintercept form is y = m x b y = m x b, where m m is the slope and b b is the yintercept y = m x b y = m x b Find the values of m m and b b using the form y = m x b y = m x bC) for drawing the graph and we use the gradient to calculate the second point The gradient of a line is the measure of steepnessAnswer and Explanation 1 We have to graph the given line Since y−2= 5(x−1) y − 2 = 5 ( x − 1) , then the line passes through the point A(1,2) A ( 1, 2) When x = 0 x = 0 we have that y

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2y=x2 Geometric figure Straight Line Slope = 1000/00 = 0500 xintercept = 2/1 = 0000 yintercept = 2/2 = 1 Rearrange Rearrange the equation by subtracting what is to theIn this Mathematics video we cover Mathematics JSS2 Straight Line Graph with specific highlights like y = mx cPlease feel free to ask your ques2 Complete the table of values and plot the graph of y = 2x – 4 3 Show that line A and line B are parallel Line A 3y 6x – 15 = 0 and Line B y = 2x 10 4 Prove that the following straight lines are perpendicular Line A y = 5 and Line B 3y – 2x 18 = 0 5

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Graph y=2 y = 2 y = 2 The slopeintercept form is y = mx b y = m x b, where m m is the slope and b b is the yintercept y = mx b y = m x b Find the values of m m and b b using the form y = mxb y = m x b m = 0 m = 0 b = 2 b = 2Plotting Straight Line Graphs If you need to draw a straight line graph, here is an easy method of how to do it Write down 3 values for x you want to use I like to use 2, 0, 2 Work out the value for y with these x values Plot the coordinates on the graph Check your points are perfectly straight and use a ruler to draw the line through themStraight Line Equations (CIE) Dr Shwe Kyaw 551 AM 1 (CIE 12, s, paper 11, question 7) The table shows values of variables x and y x 1 3 6 10 14 y 25 45 0 – –56 (i) By plotting a suitable straight line graph, show that y and x are related by the equation y

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Straight line graphs The graph of each of these equations is a straight line \x = 3\ \y = 2\ \y = x\ \y = 2x\ \y = 3x 1\ \x y = 3\ \3x – 4y = 12\ \y – 2 = 3(x 4) \If we graph the points determined by these ordered pairs and pass a straight line through them, we obtain the graph of all solutions of y = x 2, as shown in Figure 73 That is, every solution of y = x 2 lies on the line, and every point on the line is a solution of y = x 2 The graphs of firstdegree equations in two variables are alwaysA straight line on a semilog graph of y versus x represents an exponential function of the form y = a e b x A straight line on a loglog graph of y versus x represents a power law function of the form y = a x b To find the constants a and b, we can substitute two widelyspaced points which lie on the line into the appropriate equation

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A straight line graph is a visual representation of a linear function It has a general equation of y=mxc Where m is the gradient of the line And c is the y intercept Eg y=2x1 Here we can see that the gradient = 2 , and the y intercept happens at (0,1)Let f(x)=x^22x2,the straight line L intersects the graph y=f(x) at M and NThe slope and the yintercept of L are m and 1 respectively 1)Solutions for the assessment Straight line graphs 1) x = 0 or yaxis 2) A x = −

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EQUATION y = mx b m = slope of line = ∆y ∆x b = yintercept value of y where the line crosses the xaxis, ie, value of y when x =0 The equation of this line is readily gotten from the plot As shown in the graph to the right, find two points on the line (x1,y1) and (x2,y2) where you can easily determine the values of x and y Then ∆Calculate the Straight Line Graph If you know two points, and want to know the y=mxb formula (see Equation of a Straight Line ), here is the tool for you Just enter the two points below, the calculation is done liveIt means that every coördinate pair (x, y) that is on the graph, solves that equation (That's what it means for a coördinate pair to be on the graph on any equation) Every coördinate pair (x, y) on that line is (x, 2x 6) That line, therefore, is called the graph of the equation y = 2x 6 And y = 2x 6 is called the equation of that line Every first degree equation has for its graph a straight line

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Y = mx b, where m = y 2 − y 1 x 2 – x 1 \frac{y_2y_1}{x_2 – x_1} x 2 – x 1 y 2 − y 1 Here m = (24)/(1(2)) = 2/3 We can find the equation (by solving first for "b") if we have a point and the slope So we need to choose one of the points and use it to solve for b Using the point (–2, 4), we get 4 = (– 2/3)(–2) b 4 = 4/3 bY = 2x 3 x xy = 2x3 Y = 2X 3, whe re Y = xy and X = x Plot the straight line on the same axes and identify the point of intersection The two graphs intersect at the point where X = –03 Find the value of y using the Xcoordinate Since X = x = –03, Y = 2(–03) 3 Y = 24 y = –8Horizontal line graph sometimes also called a row graph A line parallel to the xaxis is called a vertical line Straight Line Graph A line graph is a graph formed by segments of straight lines that join the plotted points that represent given data The line graph is used to solve changin g conditions, often over a certain time interval A

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Draw the graph of equation x2y−3=0 F rom the graph, the value of x, when y =−2 is The number of triangles that the four lines y = x 3, y = 2 x 3, y = 3 x 2, and y x = 3 form is?The intercept/gradient form is y = mx b, where m = gradient and b = the yintercept so y = 2*(x 2) >The gradient/slope of the line is 2, which as a fraction is 2 1 2 1 \bf {\frac {2} {1}} 12 When you have two points on a straight line (x1,y1) , (x2,y2) , the gradient is y2−y1 x2−x1 y 2 − y 1 x 2 − x 1 \bf {\frac {\boldsymbol {y}2\boldsymbol {y}1} {\boldsymbol {x}2\boldsymbol {x}1}} x2−x1y2−y1

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Crosses the x and y axes ∙ let x = 0, in the equation for yintercept ∙ let y = 0, in the equation for xintercept x = 0 → y = 0 −2 = −2 ← yintercept y = 0 → 4x −2 = 0 → x = 1 2 ← xintercept plot (0, − 2),( 1 2,0) and draw a straight line through them graph {4x2 10, 10,Draw the line y = 2 on the diagram Reflect points D, E and F in the line y = 2 If we are given a rule connecting x and y (and possibly some numbers) we can draw a graph to represent this equation For example, suppose we are given the rule y = x First we try to write down some pairs of values for x and y which fit the rule eg xIf = 2 thenFinding the equation of a straight line Given the graph of a straight line, there are several ways to find its equation Method 1 This method works only if the y intercept is visible Find any two points, (x 1, y 1) and (x 2, y 2), on the line and substitute their coordinates into the following formula to get m Get b from inspection of the y intercept of the graph

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Y = 2x 4 so m = 2 the yintercept = 4 To find the xintercept we can make y = 0 0 = 2x 4 2x = 4 x = 4/2 = 2 the xintercept = 2What is a straight line graph?5 Section 122 Using Graphs of Quadratic Functions to solve Equations The following is the graph for the equation y = x2 x – 6 This graph can be used to solve the equation x2 x – 6 = 0 The solution of the equation y = x2 x – 6 are found by finding the values of x when y = 0 This is done by observing where the graph crosses the x – axis

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This is the graph of \(y = 3x 1\) Sketching straight line graphs If you recognise that the equation is that of a straight line graph, then it is not actually necessary to create a table of valuesMove the m and b slider bars to explore the properties of a straight line graph Look at The effect of changes in m;The effect of changes in b;

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Straight line graphs wwwnaikermathscom 2 Given that f(x) = x2 – 6x 18, x 0, (a) express f(x) in the form (x – a)2 b, where a and b are integers(3) The curve C with equation y = f(x), x 0, meets the yaxis at P and has a minimum point at Q (b) Sketch the graph of C, showing the coordinates of P and Q(4) The line y = 41 meets C at the point R2 2 (Problem # 45, p 53) When logy is graphed as a function of x, a straight line resultsGraph the straight line given by the following two points (x1;y1) = ( 2;3) (x2;y2) = (1;1)on a loglinear plot The functional relationship between x and y is y = (Note The original xy coordinates are given) Answer to Problem # 2 The slope of the line in the loglinear plane is

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