What is the equation in point-slope form for the line parallel to y = 4x – 14 that contains p(–2, –6)? a. y – 6 = 4(x + 2) b. x + 6 = –4(y + 2) c. y + 6 = 4(x + 2) d. y + 6 = –4(x + 2)

Point t slope form:
y + y value = m (x + x value) where m is the gradient
Parallel line must have the same gradient as the two lines never meet, so the gradient must be 4. This eliminates option B and D.
Remember that point-slope form is still an equation, so the values of both sides must be equal. So let's substitute the given coordinates.
Option A:
y-6=4(x+2)
-6-6 (-12) does not equal to 4(-2+2) (0)
Option C:
y+6=4(-2+2)
-6+6 (0) = 4(-2+2) (0)
Therefore, option C is your answer.

- Point slope form is y - b = m(x - a), where m is the slope and (a, b) is a point on the line.
- Parallel lines have the same slope

The given equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. m in y = 4x - 14 is 4; our equation in point-slope form will have 4 as m.
We have the slope (4), so now we have to add the "point on the line" which is given: P(-2, -6). That's all the information needed to write an equation in point-slope form that's parallel to y = 4x - 14; all that's left is to substitute and simplify.

y - b = m(x - a)
y - (-6) = 4(x - (-2))
y + 6 = 4(x + 2)

C. y + 6 = 4(x + 2)