It is possible to identify the gradient and y-intercept when the equation is written in the form y = mx + c
Linear equations can be rearranged in order to reveal the gradient and y-intercept.
By substituting in values for one variable, you can find a corresponding values for the other.
These pairs of values can be plotted to give the graph of the equation.

Common misconception

Only two pairs of coordinates are needed to plot a linear graph.

Whilst true, this can cause issues if one pair of coordinates is calculated incorrectly. Encourage pupils to check a third point to ensure they are correct.

Keywords

Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
Gradient - The gradient is a measure of how steep a line is.
Intercept - An intercept is the coordinate where a line or curve meets a given axis.

Task 2 contains equations that look similar but differ in key ways. Pupils could draw the graphs for these equations using software so they can see how the graphs change in relation to the equations.

Teacher tip

Licence

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Worksheet

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Starter quiz

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6 Questions

Q1.

Match each point to its correct coordinates.

Correct Answer:A,(4, -2)

(4, -2)

Correct Answer:B,(2, -4)

(2, -4)

Correct Answer:C,(-2, -4)

(-2, -4)

Correct Answer:D,(-4, -2)

(-4, -2)

Correct Answer:E,(-4, 2)

(-4, 2)

Correct Answer:F,(-2, 4)

(-2, 4)

Q2.

In algebra, when you replace variables with values you call this ...

calculating

evaluating

expanding

Correct answer: substituting

solving

Q3.

This is a table of values for a linear equation, but there is an error. Which value is the error?

$$y = 19$$

$$ y = 14$$

Correct answer: $$y = 10$$

$$y = 4$$

$$y = -1$$

Q4.

You are given the linear equation $$y=3x +4$$. When $$x=2$$, $$y$$ is .

Correct Answer: 10, y=10, ten

Q5.

You are given the linear rule $$y= 5 - 2x $$. When $$x=-4$$, $$y$$ is .

Correct Answer: 13

Q6.

Which of these could represent an $$x$$-intercept?

Correct answer: (-2, 0)

(0, -3)

(0, 6)

Correct answer: (4, 0)

(5, -5)

Exit quiz

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6 Questions

Q1.

Which of these is the $$x$$-intercept of the line $$2x + 3y = 6$$?

(0, 2)

(0, 3)

(2, 0)

(2, 3)

Correct answer: (3, 0)

Q2.

Which of these is the $$y$$-intercept of the line $$2x + 3y = 6$$?

Correct answer: (0, 2)

(0, 3)

(2, 0)

(2, 3)

(3, 0)

Q3.

Which of these coordinates are on the line with equation $$y = 10-3x$$?

(-4, -2)

Correct answer: (-3, 19)

(0, -3)

(1, 9)

Correct answer: (2, 4)

Q4.

Which of these is the correct graph for the line with equation $$2x + y = 8$$? Each square represents 1 unit on each axis.

Correct Answer: An image in a quiz

Q5.

Match each equation of a line to its key features.

Correct Answer:$$y = 10-8x$$,gradient -8 and $$y$$-intercept (0, 10)

gradient -8 and $$y$$-intercept (0, 10)

Correct Answer:$$y = 8x + 10 $$,gradient 8 and $$y$$-intercept (0, 10)

gradient 8 and $$y$$-intercept (0, 10)

Correct Answer:$$y =10x - 8 $$,gradient 10 and $$y$$-intercept (0, -8)

gradient 10 and $$y$$-intercept (0, -8)

Correct Answer:$$y = 8 - 10x $$,gradient -10 and $$y$$-intercept (0, 8)

gradient -10 and $$y$$-intercept (0, 8)

Correct Answer:$$y =8x - 10 $$,gradient 8 and $$y$$-intercept (0, -10)

gradient 8 and $$y$$-intercept (0, -10)

Q6.

The gradient of the line with equation $$2y = 4x -6$$ is .

Correct Answer: 2, two