Part 04 · Graphs · Card 3 of 8
y = mx + c
The equation of a straight line. The number m is the gradient and c is where the line crosses the y-axis.
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Analogy
Like a taxi fare: c is the fee when you get in, m is the price per mile.
Example
y = 2x + 3
Gradient m = 2y-intercept c = 3When x = 4: y = 2 x 4 + 3 = 11
In practice
A phone plan costing 10 pounds a month plus 0.50 per gigabyte follows y = 0.5x + 10.
Practice
Flashcards
- In y = mx + c, what do m and c mean?m is the gradient and c is where the line crosses the y-axis.
Interview questions
- Find the equation of the straight line through (0, 3) and (2, 7).
- Gradient = (7 - 3) / (2 - 0) = 2
- The line crosses the y-axis at 3
- So y = 2x + 3
- Check that (2, 7) fits: 2 x 2 + 3 = 7
Questions people ask
What is the y-intercept?
The y-intercept is the point where a line crosses the y-axis. On that axis x is zero, so the intercept is the value of y when x = 0. In y = 2x + 3 it is 3, so the line passes through the point (0, 3).
How do you find the equation of a line from a graph?
Read the y-intercept for c. Then pick two clear points to work out the gradient m by dividing the rise by the run. Put both into y = mx + c. A line crossing at 3 and going up 2 per step is y = 2x + 3.