Question

Write an equation for the line parallel to y = –7x + 15 that contains P(9, –6).

a.
x + 6 = 7(y – 9)
c.
y – 6 = –7(x – 9)
b.
y + 6 = 7(x – 9)
d.
y + 6 = –7(x – 9)

Answer 1

The equation for a line is y = mx + b, where m is the slope and b is the y-intercept.

The slope of the given line y = -7x + 15 is m = -7 (and its y-intercept is (0, 15) ).

Lines that are parallel have the same slope, so a line parallel to y = -7x + 15 must also have a slope of m = -7.

First way to do this
If we know the slope m = -7 and we're given two points, then we can find the y-intercept (by plugging in m = -7 and the given points) and therefore the equation of the line.
y = mx + b
(-6) = (-7)(9) + b
-6 = -63 + b
b = 57
The equation of the line would be y = -7x + 57.

Second way to do this: with point-slope formula
We can use point-slope formula to find the equation of a line if we know the slope and one of the points on the line.
The formula is: y - y1 = m(x - x1), where m is the slope and the given point is (x1, y1).
How do I get the point-slope formula? It comes from definition of slope, which is the change in y coordinates over change in x-coordinates.

`(y - y1)/(x - x1) = m \\`
Multiplying both sides by (x - x1), I get the point-slope formula.

`y - y1 = m(x - x1)`

Using this formula:
y - y1 = m(x - x1)
y - (-6) = (-7)(x - 9)
y + 6 = -7(x - 9)

From the answer choices, it looks like the problem wants you to use the point-slope formula method.

Answer 2

Here, Your Equation: y = -7x + 15
Compare it with, y = mx + c
Then, Slope (m) = -7

Parallel line slope would be same so = -7
Now, y - y1 = m(x - x1)
y - (-6) = -7(x - 9)
y + 6 = -7(x - 9)

In short, Your Answer would be Option D

Hope this helps!