Page 134 - MAT KS3 Y8 Cambridge CheckPoint

13.2 Equations of the form y = mx + c

13.2 Equations of the form y = mx + c

y = 2x + 3 y = −5x − 4 y = 20x − 30 y = −0.5x + 10

All these equations are in the form y = mx + c where m and c are numbers.
The values of m in these examples are 2, −5, 20 and −0.5.
The values of c are 3, −4, −30 and 10.
A graph of an equation like this will always be a straight line.

Worked example 13.2
a Complete the table of values for y = 5x + 10.

x −3 −2 −1 0 1 2 3
y 0 15 25

b Draw a graph of the straight line y = 5x + 10.
c Show that (−20, −90) is on the line but (20, 90) is not.

a x −3 −2 −1 0 1 2 3 If x = 2, y = 5 × 2 + 10 = 20
If x = 0, y = 5 × 0 + 10 = 10
y −5 0 5 10 15 20 25
If x = −1, y = 5 × −1 + 10 = −5 + 10 = 5
If x = −3, y = 5 × −3 + 10 = −15 + 10 = −5
b y
25
20 The scales on the two axes are not the same.
15
They have been chosen so that all the points can be plotted.
10
5 Plot the points and draw a line through them all with a ruler.
It should be a straight line.
0 x
–3 –2 –1 1 2 3
–5
–10
c If x = −20, y = 5 × −20 + 10 = −90
so (−20, −90) is on the line.
If x = 20, y = 5 × 20 + 10 = 110 This shows (20, 110) is on the line.
so (20, 90) is not on the line.

132 13 Graphs