Question

Give the equation of the line in point-

slope form that goes through the point
(-3,7) and is parallel to the line 4x-3y=7

Answer 1

`y-7=(4)/(3) (x+3)`

Explanation:

Hi there!

We are given the point (-3, 7)

We want to write the equation of the line containing that point, in point slope-form, and that is also parallel to 4x-3y=7

Parallel lines contain the same slope

So first, let's find the slope of 4x-3y=7

To do that, we can convert the line from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope, and b is the y intercept)

To do that, we need to isolate y on one side

So start by subtracting 4x from both sides

4x-3y=7

-4x -4x

________________

-3y=-4x+7

Divide both sides by -3

y=
`(4)/(3)x`-
`(7)/(3)`

Since 4/3 is in the place of where m should be, the slope of the line is 4/3

It is also the slope of our new line, which we are trying to find

As stated earlier, we want to write this line 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

This is where the point we were given earlier comes in. We simply need to substitute our values (of the point and the slope) into the formula to find the equation.

First, with the slope; substitute 4/3 as m in the equation

`y-y_1=(4)/(3) (x-x_1)`

Now substitute -3 as
`x_1` in the equation

`y-y_1=(4)/(3) (x--3)`

We can simplify this to:

`y-y_1=(4)/(3) (x+3)`
Now substitute 7 as
`y_1` into the equation

`y-7=(4)/(3) (x+3)`

Hope this helps!