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Question 1058333: In the city of Marble Springs, Main Street intersects some of the other avenues in town. On a coordinate grid, Main Street passes through the points (-2,17) and (-22,33). Grimes boulevard, a street that is perpendicular to Main Street, passes through the point (80,9). Write the equation of the line that represents Grimes Boulevard in slope-intercept form.
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
Find the gradient (Slope) of Main Street using the
coordinates that it intersects.
(-2, 17) and (-22, 33)
Gradient (Slope) = y2 - y1/x2 - x1
Gradient(Slope) = 33 - 17/-22 -(-2)
Gradient (Slope) = 33 - 17/-22 + 2
Gradient (Slope) = 16/-20 = -4/5
Lines that are perpendicular to one
another have gradients (slopes) that
multiply together to give -1
m1 x m2 = -1
-4/5 x m2 = -1
m2 = 5/4
Using the straight line equation:
y - b = m(x - a)
where m = 5/4 and (a,b) = (80, 9)
y - b = m(x - a)
y - 9 = 5/4(x - 80)
y - 9 = 5/4x - 100
y = 5/4x - 100 + 9
y = 5/4x - 91
This is the equation of Grimes
Boulevard in slope - intercept form.
Hope this helps :-)
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