Question

identify an equation in slope-intercept form for the line parallel to y=1/4x-7 that passes through (-2,-6)

Answer 1

Answer:

D. $y + 6 =- \frac{1}{4} (x+2)$

Step-by-step explanation:

We are given that a line is parallel to the line y=-1/4x-7 and passes through (-2, -6).

We want to write the equation of this line.

First, we need to know that parallel lines have the same slope.

In y=-1/4x-7, the slope of the line is -1/4; it is also the slope of the line parallel to it.

All of the answers in your system are written in point-slope form, which is $y-y_1=m(x-x_1)$, where m is the slope and $(x_1, y_1)$ is a point

As we already know the slope and the point, we can plug these values into the formula.

Starting with the slope; as found above, the slope is -1/4. Therefore, the equation will then be:

$y-y_1=-\frac{1}{4} (x-x_1)$

Now substitute -2 and -6 as $x_1$ and $y_1$ respectively (note: we have NEGATIVE numbers, and SUBTRACTION in the formula, so we will end up subtracting a negative).

$y--6=-\frac{1}{4} (x--2)$

We can simplify this to become:

$y+6=-\frac{1}{4} (x+2)$

Therefore, D is the answer.