Question

Write an equation of a line parallel to line GH below in slope-intercept form that passes through the point (−5, 6). Line GH is shown. G is at negative 2, 2. H is at 2, 6.

Answer 1

Answer:
y = x + 11

Explanation:
The general form of an equation is:
y = mx+c
where:
m is the slope
c is the y-intercept
1- getting the slope:
We are given that the line is parallel to GH. This means that:
slope of the line = slope of GH
We have G as (-2,2) and H as (2,6)
slope of GH = (y2-y1) / (x2-x2)
slope of GH = (6-2) / (2--2) = 1
slope of line = slope of GH =1 
Therefore, the equation on the line now becomes:
y = x + c
2- getting the y-intercept:
We are given that point (-5,6) passes through the line. This means that this point satisfies the equation of the line. So, we will substitute with this point in the equation and solve for c as follows:
y = x + c
6 = -5 + c
c = 6_5
c = 11

Based on the above, the equation of the line is:
y = x + 11

Hope this helps :)