The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

An intercept is the coordinate where a line or curve meets a given axis.

Checking and securing understanding of finding the equation of the line from coordinates

Maths

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

What is the equation of the line joining the points with coordinates $$(2, 5)$$ and $$(3, 8)$$?

$$y = $$ {{}}$$x + 15$$ is the equation of the line passing through the coordinates $$(4, 7)$$ and $$(7, 1)$$.

(0, {{}}) is the $$y$$-intercept of the line with gradient $$-2$$ which passes through the point $$(4, 3)$$.

A line has gradient $$-{2\over 3}$$ and passes through the point with coordinates $$(-6, 6)$$. The equation of this line is $$y = -{2\over 3}x +$$ {{}}.

Match each pair of coordinates with the equation of the line passing through them. 

Which of these lines have negative gradients?

This is a table of values for a linear graph. What is the missing $$y$$ value?

Which of these lines goes through the coordinates (3, 7) and (9, 7)?

Which of these coordinates lie on the line $$ y = 3x - 8 $$ ?

The point (-2, {{}}) lies on the line $$y = 7-4x$$. What is the $$y$$ coordinate of the point?

gradient $$5$$ and $$y$$-intercept $$(0, 5)$$

gradient $$-5$$ and $$y$$-intercept $$(0, 10)$$

gradient $$-{5\over 2}$$ and $$y$$-intercept $$(0, 5)$$

gradient $$-{2\over 5}$$ and $$y$$-intercept $$(0, 1)$$

gradient $${2\over 5}$$ and $$y$$-intercept $$(0, 1)$$

gradient $${5\over 2}$$ and $$y$$-intercept $$(0, 5)$$

Match each equation of a straight line to its key features. 

This lesson will be removed by end of Summer Term 2025.

Checking and securing understanding of finding the equation of the line from coordinates

Lesson outcome

This lesson will be removed by end of Summer Term 2025.