Question

Find the equation of the line through (2,9)(1,6)(-7,-6)

Answer 1

y=(3/2)x+6

If your equation is in a different form, let me know.

Explanation:

So the slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

Parallel lines have the same slope, m (different y-intercept (b) though).

So we need to find the slope going through (1,6) and (-7,-6).

To do this you could use
`m=(y_2-y_1)/(x_2-x_1)`.

Or, what I like to do is line the points up vertically and subtract vertically then put 2nd difference over first difference. Like so:

( 1 , 6)

-( -7, -6)

---------------

8 12

So the slope of our line is 12/8.

Let's reduce it! Both numerator and denominator are divisible by 4 so divide top and bottom by 4 giving 3/2.

Again parallel lines have the same slope.

So we know the line we are looking for is in the form y=(3/2)x+b where we don't know the y-intercept (b) yet.

But we do know a point (x,y)=(2,9) that should be on our line.

So let's plug it in to find b.

y=(3/2)x+b with (x,y)=(2,9)

9=(3/2)2+b

9=3 +b

Subtract 3 on both sides:

9-3=b

6=b

So the equation in slope intercept form is y=(3/2)x+6