Question

How do you write the equation of a line in slope intercept, point slope and standard form given Point: (5,-8) and is parallel to y=9x+4?

Answer 1

Slope intercept form of the equation is `y=9x-53`, point slope form is `y+8=9(x-5)`, and standard form is `-9x+y=-53`

Explanation:

Lines that are parallel have the same slope. Knowing this, the slope is `9`, so `m=9` in each of the forms

Slope intercept form: `y=mx+b`

First plug in the slope:

`y=9x+b`

Next we have to solve for `b` which is done by plugging in the point that was given `(5,-8)` for `x` and `y`:

`-8=9(5)+b`

`-8=45+b`

`b=-53`

Now that we know b, we can plug it in to the slope intercept form, giving us `y=9x-53`

Point slope form: `y-y_1=m(x-x_1)`

Plug in the slope, which is `9`

`y-y_1=9(x-x_1)`

Plug the point that is given, `(5,-8)`, into the point slope form:

`y-(-8)=m(x-(5))`

Simplify, giving you the final answer for point slope form:

`y+8=9(x-5)`

Finally, standard form which is `ax+by=c`

To get standard form we can use slope intercept form which we know is

`y=9x-53`

Subtract `9x` from both sides, giving you standard form:

`-9x+y=-53`