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Linear Graphs to Equations
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Linear Graphs to Equations
A straight-line equation can be written as y = mx + c. The gradient is m = change in y ÷ change in x. The y-intercept, c, is the value of y when x = 0. Use the coordinates in the questions to find how these values describe a line.
1.A line passes through the points (0,1) and (2,5). What is its y-intercept, and what is its gradient?
2.A line passes through the points (0,1) and (2,5). Find its gradient and y-intercept, then write its equation in the form y = mx + c.
3.A line passes through the points (0,4) and (4,−4). Calculate its gradient, then state its y-intercept.
4.A line passes through the points (0,4) and (4,−4). Find its gradient and y-intercept, then write its equation in the form y = mx + c.
Use coordinates to build equations
For each question, find the gradient using the two points, then use a point with x = 0 to identify the y-intercept where possible.
5.A line passes through (0, −2) and (3, 4). Find its gradient and write its equation in the form y = mx + c.
6.A line passes through (0, 5) and (2, 1). Find its gradient and equation.
7.The equation of a straight line is y = 3x − 1. What is y when x = 4? Show the substitution.
8.A line crosses the y-axis at 2 and goes down 3 units for every 1 unit it moves right. Choose its equation.
- y = 3x + 2
- y = −3x + 2
- y = −2x + 3
- y = 2x − 3
9.True or false: For the equation y = 4x − 3, the gradient is 4 and the y-intercept is −3.
TrueFalse
10.In your own words, explain how to find the gradient from two points, then how to use the gradient and y-intercept to write an equation.
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