Question

Write the equation for the line that passes through (-5, -4) and (3, 12)

Answer 1

I believe it is y=2x+6.

Answer 2

`y=2\,x+6`

Explanation:

Start by finding the slope of the segment that joins the two given points, using the slope formula:

`slope=(y_2-y_1)/(x_2-x_1) =(12-(-4))/(3-(-5)) =(16)/(8) =2`

Now, you can write the general equation of the line in slope-intercept form as:

`y=m\,x+b\\y=2\,x+b`

and find the line's y-intercept (b) by using either one of the given points - for example (3, 12):

`y=2\,x+b\\12=2\,(3)+b\\12=6+b\\b=6`

Therefore, the equation of the line is:

`y=2\,x+6`