Straight Line Graphs
Straight line graphs are an important GCSE Algebra topic. You need to understand gradient, intercepts, plotting lines and equations in the form y = mx + c.
y = mx + c
m is the gradient.
c is the y-intercept.
Gradient
The gradient tells you how steep a line is. A positive gradient slopes upwards from left to right. A negative gradient slopes downwards.
Example 1: Find the gradient
A line goes through the points (1, 3) and (4, 9).
Change in y:
9 - 3 = 6
Change in x:
4 - 1 = 3
Gradient:
6 ÷ 3 = 2
The gradient is 2.
The y-intercept
The y-intercept is where the line crosses the y-axis. In y = mx + c, the y-intercept is c.
Example 2: Identify gradient and intercept
For the line y = 3x + 5:
gradient = 3
y-intercept = 5
Plotting straight line graphs
To plot a straight line, make a table of values, plot the points and join them with a straight line.
Example 3: Plot y = 2x + 1
Choose values of x and calculate y:
If x = 0, y = 1
If x = 1, y = 3
If x = 2, y = 5
Plot the points (0, 1), (1, 3) and (2, 5).
Finding the equation from a graph
To find the equation of a straight line, find the gradient and the y-intercept.
Example 4: Find the equation
A line has gradient 4 and crosses the y-axis at 2.
Use y = mx + c:
y = 4x + 2
Horizontal and vertical lines
Horizontal and vertical lines have special equations.
Horizontal lines have equations like y = 4.
Vertical lines have equations like x = 3.
Example 5: Identify special line equations
A horizontal line crosses the y-axis at 7.
Equation: y = 7
A vertical line crosses the x-axis at -2.
Equation: x = -2
A common mistake is mixing up gradient and intercept. In y = mx + c, the number multiplying x is the gradient, and the number added at the end is the y-intercept.
If you are finding the gradient from a graph, choose two clear points where the line passes exactly through grid intersections.
Video explanation
A short Worthing Maths Tutor video explanation for straight line graphs can be embedded here later to improve student engagement and time on page.
Practice questions
- Find the gradient of a line through (2, 5) and (4, 9).
- For y = 6x - 3, state the gradient and y-intercept.
- Find the y-value when x = 4 in y = 2x + 7.
- Write the equation of a line with gradient 5 and y-intercept 1.
- Write the equation of a horizontal line crossing the y-axis at -4.
Answers
- 2
- Gradient 6, y-intercept -3
- 15
- y = 5x + 1
- y = -4
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