Question

Use the point–slope formula to write an equation of the line that passes through −4,15 and has a slope of m = − 4. Write the answer in slope–intercept form (if possible).

The equation of the line is_____

Answer 1

Let's split this problem into several steps:

Let's first put it into the point-slope form:

⇒ Point-slope form ⇒
`(y-y0)=m(x-x0)`

• (x0,y0) --> any point on the line
• m --> slope

Consider the information given:

• (x0,y0) --> (-4,15)
• m --> -4

Let's plug the numbers in:

`y - 15=-4(x+4)\\`

To put this format into slope-intercept form, we will solve for y:

⇒as in, move everything else to one side and y by itself on the other

`y - 15=-4(x+4)\\y-15=-4x-16\\y = -4x-16+15\\y=-4x-1`

Thus the equation of the line is -->
`y = -4x - 1`

Hope that helps!