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

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     12So 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+b9=3       +bSubtract 3 on both sides:9-3=b6=bSo the equation in slope intercept form is y=(3/2)x+6