Question

A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?

Answer 1

`y=(1)/(3)x-8`

Explanation:

Slope-intercept form of an equation is written as
`y=mx+b`, where
`m` is the slope and
`b` is the y-intercept.

The slope of a line that passes through the points
`(x_1,\: y_1)` and
`(x_2, \: y_2)` is
`m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)`. Using the coordinates
`(6,-6)` and
`(9,-5)` as given in the problem, we have slope of this line to be:

`m=(-5-(-6))/(9-6)=(1)/(3)`.

Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:

`-6=(1)/(3)(6)+b, \\ b=-8`

Therefore, the equation of this line in slope-intercept form is
`\fbox{$y=(1)/(3)x-8$}`.