Question

The graph of which line intersects the graph of y + 10 = -5(x - 1) in only one point?

Answer 1

A

First, I’m going to the line is question into slope intercept form.
y + 10 = -5x + 5
y = -5x + 5 -10
y = -5x -5
y + 10 = -5 (x - 1) becomes y = -5x -5 in slope intercept form. I will call this line ‘line 1’

A becomes y = 5x -15 in slope intercept form
B becomes y = -5x + 25 in slope intercept form
C becomes y = -5x -5 in slope intercept form
D becomes y = -5x + 10 in slope intercept form

C is the same line as line 1. Any point that is on line 1 is also on line C, so C cannot be it.

Notice that line B and D have the same slope but different y-intercepts as line 1. That means these lines are parallel (not the same line though - different y intercepts) to line 1, so they will never intercept.

Line A has a different slope vs line 1, so they will eventually intersect only once