Question

Write the equation for the line parallel to y=-4x-6 that goes through (4,7).

Answer 1

y = -4x + 23

Explanation:

Our task is to write the equation for the line that's parallel to y = -4x - 6 that goes through (4,7).

To write the equation, we need to know the slope of the line. We're given that it's parallel to y = -4x - 6. That is what will help us find it.

You may recall that parallel lines have equal slopes. Since they're parallel, the slope of the other line is -4.

So now we know the slope. We're also given a point that it goes through: (4,7).

We can plug this information into point-slope:

`\rm{y-y_1=m(x-x_1)}`

Replace y_1 with 7, m with -4, and x_1 with 4:

`\rm{y-7=-4(x-4)}`

This is the complete point-slope equation. See below for slope-intercept.

`\dotfill`

SLOPE - INTERCEPT

Now is the time for the slope-intercept equation.

We will take our point-slope equation...

`\rm{y-7=-4(x-4)}`

...and convert it to slope-intercept! !

Distribute -4:

`\rm{y-7=-4x+16}`

Add 7 to both sides:

`\rm{y=-4x+16+7}`

`\rm{y=-4x+23}`

Answer 2

y = -4x + 23

Explanation:

Pre-Solving

We are given that a line has the equation y = -4x - 6

We want to find the equation of the line parallel to this line and that passes through the point (4,7).

Recall that parallel lines have the same slope.

Notice how the line y = -4x - 6 is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.

This means the slope will be the value of m. We can see that -4 is where m is, so the slope of this line is -4.

The slope of the line parallel to this line is also -4.

Solving

As we found the slope of the parallel line, we can plug it into the equation for slope-intercept form.

We so far have:

y = -4x + b

Now, we need to find b.

As the equation passes through the point (4,7), we can use its values to help solve for b.

Substitute 4 as x and 7 as y.

7 = -4(4) + b

Multiply.

7 = -16 + b

Add 16 to both sides.

23 = b

Substitute 23 as b.

y = -4x + 23