Coordinate Geometry

[swerve]

Line A has a slope of -5/3 and passes through the point (–2, 7). What is the x-intercept of Line A?

A. 2 1/3
B. 2 1/5
C. 2 2/3
D. 2 2/5
E. 2 3/5

The OA is B

Source: Magoosh

[Scott@TargetTestPrep]

Line A has a slope of -5/3 and passes through the point (–2, 7). What is the x-intercept of Line A?

A. 2 1/3
B. 2 1/5
C. 2 2/3
D. 2 2/5
E. 2 3/5

The OA is B

Source: Magoosh

The equation of Line A is y = (-5/3)x + b.

Let’s now plug in (-2,7) to determine b:

7 = (-5/3)(-2) + b

7 = 10/3 + b

Multiplying by 3, we have:

21 = 10 + 3b

11 = 3b

11/3 = b

Thus, we have:

y = (-5/3)x + 11/3

We can substitute 0 for y to determine the x-intercept, and we have:

0 = (-5/3)x + 11/3

-11/3 = -5x/3

-11 = -5x

x = -11/-5 = 11/5 = 2 1/5

Answer: B