Gradient (SQA National 5 Applications of Mathematics): Revision Note

Make sure that the horizontal distance and the vertical height are measured in the same units.

The diagram shows a child's slide.

The start of the slide is 2 metres above the ground. The end of the slide is 20 centimetres above the ground.

Calculate the gradient of the slide.

Answer:

Convert all lengths to centimetres

• Multiply metres by 100

1.2 m = 120 cm

2 m = 200 cm

Identify the right-angled triangle

Find the vertical height of the triangle

• Subtract the height of the end from the height of the start

200 cm - 20 cm = 180 cm

Use $\mathrm{gradient}=\frac{\mathrm{vertical}\mathrm{height}}{\mathrm{horizontal}\mathrm{distance}}$

$\frac{180}{120}=1.5$

Gradient = 1.5

Jerry draws a line of best fit on a scattergraph. The line goes through the points $\left(4,11\right)$ and $\left(12,17\right)$.

Calculate the gradient of the line of best fit.

Answer:

Sketch the two points and draw a right-angled triangle

Find the horizontal distance using the $x$ coordinates

$12-4=8$

Find the vertical height using the $y$ coordinates

$17-11=6$

Use the formula is $\mathrm{gradient}=\frac{\mathrm{vertical}\mathrm{height}}{\mathrm{horizontal}\mathrm{distance}}$

$\frac{6}{8}=0.75$

Gradient = 0.75