Coordinates Picture For each instruction, join up the coordinates. Do not join one instruction to the next. a. (1, 3) (0, 3) (0, 5) (2, (10, 5) (10, 3) (8, 3) b. (6, 2) (6, 4) (8, 4) (8, c. (1, 2) (1, 4) (3, 4) (3, d. (3, 3) (6, 3) e. (2, 5) (3, 6) (6, 6) (7, 7) (6, 7) (7, 6) 2) (6, 2) 2) (1, 2) 5) (2, 5) Given an equation, we can find coordinate points for that equation by constructing a table of values. Suppose we want to plot points for: y=x+3 We can use a table as follows: x 3 2 1 0 1
2 3 y = x +3 0 1 2 3 4 5 6 (2, 5) (3, 6) (3, 0) (2, 1) (1, 2)
(0, 3) (1, 4) x 1) Complete a table of values: 3 2 1 0 1 2 y = x +3 2) Plot the points on a coordinate grid. 0 1 3
2 4 3 5 6 (3, 0) (2, 1) (1, 2) (0, 3) (1, 4) (2, 5) (3, 6) y 3) Draw a straight line through the points. 1 0 9 8 4) Label the line. y=x+3 7 6 5 4 3
2 1 10 9 8 7 -6 -5 -4 -3 -2 0 -1 1 2 3 -4 -5 -6 -7
-8 -9 1 0 1 2 3 4 5 6 7 8 9 1 0 x x 1) Complete a
table of values: 3 2 y = 3x + 1 -8 1 -5 0 -2 1 1 2 4 3 10 7 (-3, -8)(-2, -5)(-1, -2) (0, 1) (1, 4) (2, 7) (3, 10) y
2) Plot the points on a coordinate grid. 1 0 9 3) Draw a straight line through the points. y = 3x + 1 8 7 6 4) Label the line. 5 4 3 2 1 10 9 8
7 -6 -5 -4 -3 -2 0 -1 1 2 3 -4 -5 -6 -7 -8 -9 1 0 1 2
3 4 5 6 7 8 9 1 0 x x 3 2 1 0 1
2 3 1) Complete a table of values: 2) Plot the points on a coordinate grid. y 1 0 9 3) Draw a straight line through the points. 8 7 6 4) Label the line. 5 4 3 2 1 10
9 8 7 -6 -5 -4 -3 -2 0 -1 1 2 3 -4 -5 -6 -7 -8 -9 1 0
1 2 3 4 5 6 7 8 9 1 0 x How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity Finished? Sketch these in your book on your own axes! 5) y = 2x 4
6) y = 3x + 2 7) y = x Pair Activity Match the equations on the dominoes to the coordinates that are on the line! Hint: Draw a table of values for each question. Extension: Can you sketch any of them? How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity What can you tell me about the following pairs of linear equations? y = 2x + 4 y = x + 4 y = x 3 y = -2x + 6 y = 3x + 2 y=x-1 y = 4x 2 y = 4x + 1 We are learning to calculate the equation of a linear graph from two coordinates.
What can you tell me about y = mx + c Gradient (the slope of the line) Y intercept (where the graph cuts the y-axis) Calculate the gradient of the line which passes through (2, 6) and (4, -2). Start by calculating the gradient. (2, 6) 8 rise =8 =4 run 2 2 (4, -2) The graph slopes downwards so the gradient is negative. m = -4 The gradient is rise run
But you also need to think about whether its +ve or ve. Calculate the gradient of the line which passes through (7, 12) and (15, 32). Start by calculating the gradient. (15, 32) 20 (7, 12) 8 rise =20 =5 run 8 2 The graph slopes upwards so the gradient is positive. m=5 2 The gradient is rise run But you also need to think about whether its +ve or ve. Calculate the gradients of the lines which pass through the following pairs of points (3, 6) and (5, 12)
(2, 6) and (10, 10) (4, 9) and (1, 15) (2, 1) and (5, 10) (-1, 3) and (3, -1) (2, 7) and (3, 4) (3, 5) and (5, 1) (4, 2) and (3, -4) (2, 1) and (-3, 5) (2, 7) and (6, -1) (3, 1) and (6, -8) (-2, 3) and (-5, -2) (4, 3) and (8, 5) (5, 8) and (1, 5) (6, -1) and (-3, 2) Remember to sketch each pair of coordinates and this about the sign!
Extension: Does the line y = 3x + 2 go through (-2, -3)? How do you know? Calculate the gradients of the lines which pass through the following pairs of points 3 -2 3 -1 -3 -2 6 -4/5 -2 -3 5/3
-3 Remember to sketch each pair of coordinates and this about the sign! Extension: No substitute x = -2 and y = -4, not -3 Find the equation of the line which passes through (2, 6) and (4, -2). We found earlier that the gradient was 4. We now need the y-intercept. y = -4x + c 6 = -4(2) + c 6 = -8 + c 14 = c y = -4x + 14 Substitute the gradient and one of the coordinates (x and y) into y = mx + c. Find the equation of the line which passes through (7, 12) and (15, 32). We found earlier that the gradient was 5. 2 We now need the y-intercept. y = 5x + c 2
12 = 5(7) + c 2 12 = 35 + c 2 -9 = c 2 y = 5x 9 2 2 Substitute the gradient and one of the coordinates (x and y) into y = mx + c. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity Finished? Complete the extension activity! RAG Answers 1) y = 2x + 4 2) y = 5x 2 3) y = 4x 14 4) y = 5x 1 5) y = -2x + 6 6) y = -x + 2 Spot the mistake
Find the equation of the line which passes through (9, 2) and (3, 7). rise =6 = 2 run 9 3 y = 2x + c 3 2 = 2(9) + c 3 2=6+c -4 = c y = 2x 4 3