Question

Write the equation of the line that passes through the points (−3, 5) and (2, -10) in slope-intercept form.​

Answer 1

`y=-3x-4`

Explanation:

Hi there!

Slope intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where the two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (−3, 5) and (2, -10)

`m=(-10-5)/(2-(-3))\\m=(-10-5)/(2+3)\\m=(-15)/(5)\\m=-3`

Therefore, the slope is -3. Plug -3 into
`y=mx+b` as m:

`y=-3x+b`

2) Determine the y-intercept (b)

`y=-3x+b`

Plug one of the given points, (−3, 5) or (2, -10) into the equation and isolate b

`5=-3(-3)+b\\5=9+b`

Subtract 9 from both sides

`5-9=9+b-9\\-4=b`

Therefore, the y-intercept is -4. Plug -4 into
`y=-3x+b` as b:

`y=-3x-4`

I hope this helps!