Question

Write the equation of the line that passes through the points (-3,-8) and (6,-4).

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

Answer 1

The equation in point-slope form is:
`\mathbf{y+8= (4)/(9)(x+3)}`

Explanation:

Write the equation of the line that passes through the points (-3,-8) and (6,-4)

The point slope form is:
`y-y_1=m(x-x_1)`

Where m is slope and x₁ and y₁ are the points given

Finding Slope

Slope can be found of given points using formula:
`Slope=(y_2-y_1)/(x_2-x_1)`

We have
`x_1=-3, y_1=-8, x_2=6 \ and \ y_2=-4`

Putting values and finding slope

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(-4-(-8))/(6-(-3))\\Slope=(-4+8)/(6+3)\\Slope=(4)/(9)`

So, slope m = 4/9

Using point (-3,-8) and slope m = 4/9 the equation is:

`y-y_1=m(x-x_1)\\y-(-8)=(4)/(9)(x-(-3))\\y+8= (4)/(9)(x+3)\\`

So, the equation in point-slope form is:
`\mathbf{y+8= (4)/(9)(x+3)}`