GreenlightTestPrep wrote:

What is the area of a triangle created by the intersections of the lines \(x=4\), \(y=5\) and \(y = -\frac{3}{4}x + 20\)?

A. 42

B. 54

C. 66

D. 72

E. 96

Let's first sketch the lines x = 4 and y = 5

To find the point where y = (-3/4)x + 20 intersects the line x =

4, replace x with

4 to get: y = (-3/4)

4 + 20 = 17

So the point of intersection is (4, 17)

To find the point where y = (-3/4)x + 20 intersects the line y =

5, replace y with

5 to get:

5 = (-3/4)x + 20

When we solve for x, we get x = 20

So the point of intersection is (20, 5)

Add this information to our sketch:

From here, we can determine the length of the right triangle's base and height:

Area = (1/2)(base)(height)

= (1/2)(16)(12)

= 96

Answer: E

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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