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18.1 Gradient of a graph

18.1 Gradient of a graph

Look at these two straight-line graphs. y
Both lines are sloping, but one is steeper than the other. 4 Line 1

"e steepness of a graph is described by its gradient. 3 2
2

To !nd the gradient of the line, you can draw a right-angled triangle. 1 2 3
Use part of the line itself as the hypotenuse, and position the triangle so 0 x
that its other two sides are on the coordinate grid lines. –3 –2 –1 1 2 3 4 5
–1

Find the di#erence between the x-coordinates and the y-coordinates of –2 –4
the endpoints of the line segment you have used. –3 Line 2

"e gradient is: change in y .
change in x
2

"e gradient of line 1 is . The gradient of line 2 is negative
3
"e gradient of line 2 is −4 = −2. because it goes down from left to right.

2
Worked example 18.1

A straight-line graph goes through the points (0, 5) and (6, 2). Find the gradient of the graph.

Plot the points and draw the line. y 6
5
Draw a triangle. 4
3 1 –3
The gradient is − = − . 3
6 2
2
1
0 x
–1 1 2 3 4 5 6 7
–1

) Exercise 18.1 5 y

1 Calculate the gradients of line a and line b. 4
3
b
2
1
0 x
–3 –2 –1 1 2 3 4
–1
–2
–3 a
y a
2 Work out the gradients of lines a, b and c. 4
b
3
2
1
0 x
–2 –1 1 2 3 4
–1
–2
c
166 18 Graphs 18 Graphs