Question

What is the equation of the line that passes through the point (−1,−5) and has a slope of −3?

Answer 1

`y=-3x-8`

Explanation:

Linear equations are typically organized in 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) Plug the slope (m) into the equation

We're given that the slope is -3. Plug -3 into the equation

`y=-3x+b`

2) Solve for the y-intercept (b)

To solve for b, plug the given point (-1,-5) into the equation as (x,y).

`-5=-3(-1)+b\\-5=3+b`

Subtract 3 from both sides

`-5-3=3+b-3\\-8=b`

Therefore, the y-intercept is -8. Plug -8 back into our original equation as b

`y=-3x-8`

I hope this helps!