at what point does a line with a slope of 3/4 and a y-intercept of -5 intersect a line with a slope of -1/4 and a y-intercept of 3? A. (-8,1) B. (-1,8) C. (1,8) D. (8,1)

Question

A. (-8,1) B. (-1,8) C. (1,8) D. (8,1)

Answer 1

The respective equations are (slope-intercept form):

1) y = (3/4)x - 5, and

2) y = (-1/4)x +3

To find the point of intersection use the substitution method as follows:

(3/4) x - 5 = (-1/4)x +3 [replace y in one of the equations with its equivalent in terms of x]

Since I avoid working with fractions I would now multiply every term by 4 (but that is not necessary):

3x - 20 = -x +12

3x + x = 12 + 20

4x = 32

x = 8

When x = 8:

y = (3/4)(8) - 5 = 6 - 5 = 1

So, the point of intersection is at (8, 1).

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You could also substitute the coordinates of each point into each equation to determine which point satisfied both--not recommended as a strategy.