Question

Write the equation of the line that passes through the points (-5, 9) and (-2, 1).

Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.

Answer 1

`\displaystyle y=(-8)/(3)x-3(2)/(3)`

Explanation:

Slope-intercept form is y = mx + b. This is where m is the slope and b is the y-intercept.

We will be writing a point-slope equation, then simplifying it into a slope-intercept form equation. First, we need to find the slope. We find that we have a slope of
`(-8)/(3)`.

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) )=(1-9)/(-2--5) =(-8)/(3)`

Next, we will write the point-slope equation.

y -
`y_1` = m(x -
`x_1`)

y - 9 =
`(-8)/(3)`(x - -5)

y - 9 =
`(-8)/(3)`(x + 5)

y - 9 =
`(-8)/(3)`x - 13
`(1)/(3)`

y =
`(-8)/(3)`x - 3
`(2)/(3)`