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?

1 Answer
Jul 19, 2018

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