Answer:
y=(3/2)x+6
If your equation is in a different form, let me know.
Step-by-step 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 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
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
