Question

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

Answer 1

y+6= -4(x+2)

Explanation:

Answer 2

D.
`y + 6 =- (1)/(4) (x+2)`

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=-(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=-(1)/(4) (x--2)`

We can simplify this to become:

`y+6=-(1)/(4) (x+2)`

Therefore, D is the answer.