I've added some brackets to the 3rd equation to show the intent of the question.
[email protected] wrote:What is the area of a triangle created by the intersections of the lines x = 4, y = 5, and y = (−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)
= [spoiler]96 = E [/spoiler]
Cheers,
Brent
