A line in slope intercept form

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Question from laurie, a student:

the question: Write and equation of the line that passes through the point
and has the give slope. Then rewrite the equation in slope intercept form.
(2, 5 ) m= 3

i got from a website that you first have to turn it into point slope form.
so i got this
y=3x + 11

can you tell me if that is right so far, if it is can you tell me how to turn that into slope intercept form. ?

thanks :D

Laurie,

The point slope form is

y - y₁ = m(x - x₁)

where the point you are given is (x₁, y₁) and the slope is m. Substitute your point and slope to obtain the equation is point slope form.

Once you have the equation in point slope form you can manipulate the equation to put it is slope intercept form

y = mx + b.

Here is an example. Suppose that the line in point slope form is

y - 4 = 6(x - 2).

Expand the right side to obtain

y - 4 = 6x - 12.

Add 4 to each side and the equation becomes

y = 6x - 12 + 4

or

y = 6x - 8.

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.