Topics
Linear Equations
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New Zealand
Level 6 - NCEA Level 1

The Gradient Formula

Lesson
Practice

Interactive practice questions

A certain ski resort has two ski runs.

Two ski runs on a slope are labeled as Run A and Run B. Run A depicts a skier at a higher elevation with a vertical drop of $19$19 m, while Run B features a skier at a lower elevation with a vertical drop of $6$6 m. Both runs are illustrated within right-angled triangles that indicate the slope's incline, with the hypotenuses representing the ski paths. The base of the triangle for Run B measures $17$17 m, and the base of the triangle for Run A measures $25$25 m.
a

Find the gradient of ski slope $A$A. Give your answer as a decimal to two decimal places.

b

Find the gradient of ski run $B$B. Give your answer as a decimal to two decimal places.

c

Which run is steeper?

Ski run $A$A

A

Ski run $B$B

B
Easy
3min

Find the gradient of the line that passes through Point A $\left(-1,0\right)$(−1,0) and Point B $\left(0,3\right)$(0,3) using $m=\frac{\text{rise }}{\text{run }}$m=rise run ​.

Easy
1min

Find the gradient of the line that passes through Point A $\left(2,-6\right)$(2,−6) and the origin using $m=\frac{\text{rise }}{\text{run }}$m=rise run ​.

Easy
1min

Find the gradient of the line that passes through Point A $\left(3,5\right)$(3,5) and Point B $\left(1,8\right)$(1,8), using $m=\frac{y_2-y_1}{x_2-x_1}$m=y2​−y1​x2​−x1​​.

Easy
1min
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Outcomes

NA6-7

Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns

NA6-8

Relate rate of change to the gradient of a graph

91028

Investigate relationships between tables, equations and graphs

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