Question

What is the equation of this line? Picture included

Answer 1

A straight line needs two pieces of information to be identified, a gradient and a y-intercept (technically any point will do but the y-intercept is particularly convenient if we have it).

The gradient is calculated by taking two points on the line, and dividing the change in y-coordinate by the change in x-coordinate between them. I'm going to take the points (0,-3) and (2,-2).

The change in y-coordinate is (-2) - (-3) = 1

The change in x-coordinate is (2) - (0) = 2.

Gradient = m = 1/2

Next we identify the y-intercept, the value of y when x = 0. This value is -3, and we call it c.

The equation of a line in slope-intercept form is y = mx + c. Slotting in the values for m and c we have ascertained, we find that the equation of this line is:

y = (1/2)x - 3

I hope this helps :)