Question

A line contains the points (a, b) and (a + 3, b + 3). Find the equation of the line in terms of a and b in point-slope form, and then convert it to slope-intercept form.

Answer 1

• y -b = x -a
• y = x + (b-a)

Explanation:

The slope is the ratio of the change in y to the change in x:

m = ((b+3) -b)/((a +3) -a) = 3/3 = 1

The point-slope form of the equation of a line through point (h, k) with slope m is ...

y -k = m(x -h)

Here, we have (h, k) = (a, b) and m=1, so the equation in point-slope form is ...

y -b = x -a

Adding b puts this in slope-intercept form:

y = x + (b-a)