Question

What is an equation in point-slope form of the line that passes through (1, -6) and (4, 6)?

Answer 1

`y+6=4(x-1)` or
`y-6=4(x-4)`

Explanation:

We want to find the equation in point-slope form of the line that passes through the two points (1, -6) and (4, 6).

Recall that point-slope form is given by:

`y-y_(1)=m(x-x_(1))`

Where m is the slope.

Find the slope m using the two given points.

`\displaystyle m = (\Delta y)/(\Delta x) = (6-(-6))/(4-1) = (12)/(3) = 4`

Substitute. We can use either point. Using the point (1, -6), we acquire:

`y-(-6)=4(x-(1))`

Simplify:

`y+6=4(x-1)`

And using the point (4, 6), we acquire:

`y-(6)=4(x-(4))`

Simplify:

`y-6=4(x-4)`