The gradient and intercept of a line can easily be stated by looking carefully at its equation.
For the line with equation y = mx + c, the gradient is m and the intercept on
the y-axis is c.
m is the coefficient of x when in the form y = ......
c is the number on its own
Which of these graph lines best represents y = 2x - 3 ?
A B C
Comparing y = 2x - 3 to y = mx + c, we see that m = 2 and c = -3
The gradient of the line, m, is 2 and the intercept, c, is -3.
This means that it crosses the y-axis at (0, -3) and from this point we move 1 to the right and 2 up to draw the line (or 4 to the right and 8 up)
The line is shown below in red.
So B is the only possible graph line that looks like this. It has a positive gradient and a negative intercept on the y-axis.
NB Assume that the scales on each axis are the same for all questions in this worksheet.