Question

Find the slope-intercept form of the line that satisfies the given conditions.

Through A(−7, 5) and B(6, 11)

Answer 1

`y=(6)/(13)x+(107)/(13)`

Explanation:

(x1, y1) = (-7, 5)

(x2, y2) = (6, 11)

The firs thing to do is fine the slope. That is the distance between the y-coordinates divided by the distance between the x-coordinates:

`m=(y2-y1)/(x2-x1)`

I marked the points above as points 1 and 2, so you can plug those numbers into the formula:

`m=(11-5)/(6--7)\\\\m=(6)/(13)`

That fraction can't be simplified any further, so the slope of this line is 6/13. The next thing to do is to find the y-intercept.

`y=mx+b`

Plug the slope and any point of your choice into the equation. I'll use point b:

`11=((6)/(13))6+b`

Now, solve for b:

`11=(36)/(13)+b\\\\11-(36)/(13)=b\\\\(143)/(13)-(36)/(13)=b\\\\(107)/(13)=b\\\\b=(107)/(13)`

They're far from clean, but those are the correct slope and y-intercept. Using those, the equation for this line is:

`y=(6)/(13)x+(107)/(13)`

You can confirm that this is the correct equation by checking it with one of the points. Plug in one of the known values of x and make sure it gives the correct value of y:

`y=(6)/(13)(-7)+(107)/(13)\\\\y=(-42)/(13)+(107)/(13)\\\\y=(65)/(13)\\\\y=5`

That works out.