The segment that is parallel to UV is RS.
Equation in slope-intercept form, of the segment RS is: y = x + 9.
The slope of the sides of triangles that are similar to each other are the same.
Slope (m) = change in y/change in x = y2 - y1/x2 - x1
The equation of a line having slope as m and y-intercept as b, in slope-intercept form is expressed as: y = mx + b.
Given triangle QRS is similar to triangle TUV, the side that is parallel to segment UV is segment RS.
Find the slope (m) of segment UV
Slope (m) = change in y / change in x = RQ/QS = 6 units/6 units
m = 1
Substitute a point on the line (-2, 7) and m = 1 into y = mx + b to find the value of b
7 = 1(-2) + b
7 = -2 + b
7 + 2 = b
9 = b
b = 9
Substitute m = 1 and b = 9 into y = mx + b:
y = 1(x) + 9
y = x + 9
The equation in slope-intercept form, of the segment that is parallel to UV is: y = x + 9.
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