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Gradient and y-intercept

Find gradient using rise over run, calculate gradient from two points, and identify gradient and y-intercept from the equation y=mx+by = mx + b.

Worked examples

Finding gradient and y-intercept from two points on a graph

Straightforward

Problem

A straight line passes through the points (0,2)(0, 2) and (4,10)(4, 10). Find the gradient and y-intercept of the line.

Finding gradient from two points using the gradient formula

Moderate

Problem

Find the gradient of the line passing through (2,3)(2, 3) and (5,12)(5, 12).

Interpreting gradient as a rate of change in context

Challenging

Problem

A car travels at a constant speed. After 1 hour it has covered 60 km, and after 3 hours it has covered 180 km. Find the gradient of the distance-time graph and explain what it represents.

Practise

Q1·Straightforward
A line on a grid has two labelled points at (0,1)(0, 1) and (3,7)(3, 7). Find the gradient of the line using rise over run.
Q2·Straightforward
A line on a grid passes through (0,4)(0, 4) and (5,9)(5, 9). Find the gradient using rise over run.
Q3·Straightforward
A line on a grid has labelled points at (0,6)(0, 6) and (4,2)(4, 2). Find the gradient using rise over run.
Q4·Straightforward
A line passes through (0,−3)(0, -3) and (2,1)(2, 1). State the y-intercept of the line.
Q5·Moderate
Find the gradient of the line passing through (1,2)(1, 2) and (4,11)(4, 11).
Q6·Moderate
Find the gradient of the line passing through (3,1)(3, 1) and (7,9)(7, 9).
Q7·Moderate
State the gradient of the line y=4x−3y = 4x - 3.
Q8·Moderate
State the y-intercept of the line y=−3x+8y = -3x + 8.
Q9·Challenging
A straight line slopes downward from left to right. Which of the following best describes its gradient?
Q10·Challenging
Line A has gradient 14\frac{1}{4} and Line B has gradient 33. Which line is steeper?
Q11·Challenging
A water tank is being filled at a steady rate. After 2 minutes it contains 10 litres, and after 6 minutes it contains 30 litres. Find the rate at which water is entering the tank, in litres per minute.
Q12·Challenging
A horizontal line has a gradient of: