Every straight line is described by y = mx + c. Once you know what m and c do, you can sketch any line and read any graph.
A straight-line graph shows a relationship that changes at a constant rate. Its equation is always y = mx + c, and the whole topic comes down to understanding what the two letters m and c mean.
1c is where the line starts
c is the y-intercept — the point where the line crosses the vertical axis (where x = 0). If the equation is y = 2x + 3, the line crosses the y-axis at 3.
2m is how steep it is
m is the gradient — how much y changes for every 1 unit across. Gradient = change in ychange in x. A positive m slopes up to the right; a negative m slopes down.
- 1Start at the y-intercept: c = −1, so plot (0, −1).This is the guaranteed starting point.
- 2Use the gradient m = 2 = 21: go 1 right and 2 up to (1, 1).Gradient tells you the next point from the intercept.
- 3Join the two points with a straight line and extend it.Two points fully fix a straight line.
To find the x-intercept (where the line crosses the horizontal axis), set y = 0 and solve for x. For y = 2x − 1 that gives x = 12.
Don't confuse the intercepts. The y-intercept comes from x = 0; the x-intercept comes from y = 0. Mixing them up is a classic slip.
Straight-line graphs are the gateway to all of functions in Grades 10–12, and analytical geometry is built directly on gradient and intercepts — so a solid grip here pays off for years.
Practice exercises
Work each one out, then click to reveal the answer.
- 1For y = 3x + 2, give the gradient and y-intercept.
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Gradient 3, y-intercept 2 - 2For y = −x + 5, where does it cross the y-axis?
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At (0, 5) - 3Find the y-intercept of y = 4x − 7.
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−7, i.e. the point (0, −7) - 4Find the x-intercept of y = 2x − 6.
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Set y = 0: 2x − 6 = 0 → x = 3
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