Question

Which point lies on the line with point-slope equation y - 3 = 4(x + 7)?

A. (-7, -3)
B. (7, 3)
C. (-7, 3)
D. (7, -3)

Answer 1

The point (-7, 3) lies on the line with the given point-slope equation y - 3 = 4(x + 7) (option C).

What is the point that lies on a line?

To determine which point lies on the line with the given point-slope equation y - 3 = 4(x + 7), substitute the coordinates of each point into the equation and check for equality.

Let's check each point:

A. (-7, -3):

`\[(-3) - 3 \stackrel{?}{=} 4((-7) + 7)\]`

`\[-6 \\eq 0\]`

B. (7, 3):

`\[3 - 3 \stackrel{?}{=} 4((7) + 7)\]`

`\[0 \\eq 56\]`

C. (-7, 3):

`\[3 - 3 \stackrel{?}{=} 4((-7) + 7)\]`

0 = 0

D. (7, -3):

`\[-3 - 3 \stackrel{?}{=} 4((7) + 7)\]`

`\[-6 \\eq 56\]`

Therefore, the point (7, -3) does not lie on the line, but the point (-7, 3) does. So, the correct answer is C. (-7, 3).