Linear Graphs
A linear graph is a straight line on the Cartesian plane. It can be described by the equation y = mx + b, where m is the gradient and b is the y-intercept.
What You Need to Know
Key Concept Diagram
The equation y = mx + b is called slope-intercept form; m is the gradient and b is the y-intercept
To graph a line, plot the y-intercept and use the gradient to find a second point
Parallel lines have the same gradient but different y-intercepts
The x-intercept is found by setting y = 0 and solving for x
Key Vocabulary
Linear graph
A straight-line graph representing a linear relationship between two variables
y-intercept
The point where a line crosses the y-axis; found by setting x = 0
x-intercept
The point where a line crosses the x-axis; found by setting y = 0
Slope-intercept form
The equation y = mx + b, where m is the gradient and b is the y-intercept
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the y-intercept of the line y = 3x + 7?
Question 2
What is the gradient of the line y = -2x + 5?
Question 3
Where does the line y = x - 4 cross the x-axis?
Key Concepts Summary
- ●The equation y = mx + b is called slope-intercept form; m is the gradient and b is the y-intercept
- ●To graph a line, plot the y-intercept and use the gradient to find a second point
- ●Parallel lines have the same gradient but different y-intercepts
- ●The x-intercept is found by setting y = 0 and solving for x