New
New
Year 10
Higher

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

I can find the equation of the line from two coordinate pairs as well as from the gradient and one coordinate pair.

New
New
Year 10
Higher

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

I can find the equation of the line from two coordinate pairs as well as from the gradient and one coordinate pair.

Lesson details

Key learning points

  1. The gradient can be found from two points by considering the change in y over the change in x
  2. The y-intercept can be found using the gradient and one of the points.
  3. By substituting the gradient and one coordinate pair into the general equation, you can find the y-intercept.
  4. The y-intercept occurs when the x value is zero.
  5. 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.

This builds on KS3 work where pupils found equations by looking at the relationship between x and y values within a coordinate pair. Remind them that any coordinate pair on the line should satisfy their equation. They can use this to check their equations seem reasonable.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Which of these lines have negative gradients?
An image in a quiz
A (purple)
B (green)
Correct answer: C (pink)
Correct answer: D (blue)
E (black)
Q2.
This is a table of values for a linear graph. What is the missing $$y$$ value?
An image in a quiz
Correct Answer: 5
Q3.
Which of these lines goes through the coordinates (3, 7) and (9, 7)?
$$x = 3$$
$$x = 7$$
Correct answer: $$y= 7$$
$$y = 9$$
$$x + y = 10$$
Q4.
Which of these coordinates lie on the line $$ y = 3x - 8 $$ ?
(-3, 1)
(1, 5)
Correct answer: (2, -2)
(5, 9)
Correct answer: (7, 13)
Q5.
The point (-2, ) lies on the line $$y = 7-4x$$. What is the $$y$$ coordinate of the point?
Correct Answer: 15
Q6.
Match each equation of a straight line to its key features.
Correct Answer:$$y = 5x + 5$$,gradient $$5$$ and $$y$$-intercept $$(0, 5)$$

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

Correct Answer:$$y = 10 - 5x$$,gradient $$-5$$ and $$y$$-intercept $$(0, 10)$$

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

Correct Answer:$$2y + 5x = 10$$,gradient $$-{5\over 2}$$ and $$y$$-intercept $$(0, 5)$$

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

Correct Answer:$$10y + 4x = 10$$,gradient $$-{2\over 5}$$ and $$y$$-intercept $$(0, 1)$$

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

Correct Answer:$$5y = 2x + 5$$,gradient $${2\over 5}$$ and $$y$$-intercept $$(0, 1)$$

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

Correct Answer:$$y - {5\over 2}x = 5$$,gradient $${5\over 2}$$ and $$y$$-intercept $$(0, 5)$$

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

6 Questions

Q1.
What is the equation of this line?
An image in a quiz
$$y = x + 3$$
$$y = 2x - 3$$
$$y = 3x $$
$$y = 3x - 3$$
Correct answer: $$y = 4x - 3$$
Q2.
What is the equation of the line joining the points with coordinates $$(2, 5)$$ and $$(3, 8)$$?
$$y = 2x + 1$$
$$y = 2x + 2$$
$$y = 2.5x $$
Correct answer: $$y = 3x - 1$$
$$y = 3x + 3$$
Q3.
$$y = $$ $$x + 15$$ is the equation of the line passing through the coordinates $$(4, 7)$$ and $$(7, 1)$$.
Correct Answer: -2, - 2
Q4.
(0, ) is the $$y$$-intercept of the line with gradient $$-2$$ which passes through the point $$(4, 3)$$.
Correct Answer: 11
Q5.
A line has gradient $$-{2\over 3}$$ and passes through the point with coordinates $$(-6, 6)$$. The equation of this line is $$y = -{2\over 3}x +$$ .
Correct Answer: 2
Q6.
Match each pair of coordinates with the equation of the line passing through them.
Correct Answer:(5, 4) and (6, 8),$$y = 4x - 16$$

$$y = 4x - 16$$

Correct Answer:(5, 4) and (7, 1),$$2y + 3x = 23 $$

$$2y + 3x = 23 $$

Correct Answer:(5, 4) and (8, 13),$$y - 3x = -11 $$

$$y - 3x = -11 $$

Correct Answer:(-5, 4) and (-3, 7),$$2y - 3x = 23 $$

$$2y - 3x = 23 $$

Correct Answer:(-5, 4) and (-6, 3),$$y - x = 9 $$

$$y - x = 9 $$