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

Starter quiz

Which of these lines have negative gradients?

A (purple)

B (green)

C (pink) ✓

D (blue) ✓

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

'5' ✓
Which of these lines goes through the coordinates (3, 7) and (9, 7)?

$x = 3$

$x = 7$

$y= 7$ ✓

$y = 9$

$x + y = 10$
Which of these coordinates lie on the line $y = 3x - 8$ ?

(-3, 1)

(1, 5)

(2, -2) ✓

(5, 9)

(7, 13) ✓
The point (-2, ______) lies on the line $y = 7-4x$ . What is the $y$ coordinate of the point?

'15' ✓
Match each equation of a straight line to its key features.

$y = 5x + 5$

⇔

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

$y = 10 - 5x$

⇔

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

$2y + 5x = 10$

⇔

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

$10y + 4x = 10$

⇔

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

$5y = 2x + 5$

⇔

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

$y - {5\over 2}x = 5$

⇔

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

Exit quiz

What is the equation of this line?

$y = x + 3$

$y = 2x - 3$

$y = 3x$

$y = 3x - 3$

$y = 4x - 3$ ✓
What is the equation of the line joining the points with coordinates $(2, 5)$ and $(3, 8)$ ?

$y = 2x + 1$

$y = 2x + 2$

$y = 2.5x$

$y = 3x - 1$ ✓

$y = 3x + 3$
$y =$ ______ $x + 15$ is the equation of the line passing through the coordinates $(4, 7)$ and $(7, 1)$ .

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

'11' ✓
A line has gradient $-{2\over 3}$ and passes through the point with coordinates $(-6, 6)$ . The equation of this line is $y = -{2\over 3}x +$ ______.

'2' ✓
Match each pair of coordinates with the equation of the line passing through them.

(5, 4) and (6, 8)

⇔

$y = 4x - 16$ ✓

(5, 4) and (7, 1)

⇔

$2y + 3x = 23$ ✓

(5, 4) and (8, 13)

⇔

$y - 3x = -11$ ✓

(-5, 4) and (-3, 7)

⇔

$2y - 3x = 23$ ✓

(-5, 4) and (-6, 3)

⇔

$y - x = 9$ ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

The gradient can be found from two points by considering the change in y over the change in x
The y-intercept can be found using the gradient and one of the points.
By substituting the gradient and one coordinate pair into the general equation, you can find the y-intercept.
The y-intercept occurs when the x value is zero.
It is useful to check using the second point while understanding the limitations of this check.

Common misconception

Writing equations of the form y = mx + c and getting the gradient and y-intercept the wrong way round.

Graphing software can be used to show that adding a constant is a translation of the graph. Remind pupils that the y-intercept is when x is zero which is why it is the constant in the equation. They can substitute x = 0 to check.

Keywords

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