Question

Find the equation of the line using the point-slope formula. Write all the final equations

using the slope-intercept form.

Answer 1

`y=(1)/(2)x+(5)/(2)`

Explanation:

We are going to find the slope by lining up the points vertically and subtract, then put 2nd difference over first.

Also you could just use
`(y_2-y_1)/(x_2-x_1)`. It is the same thing.

( 5 , 5)

-( 1 , 3)

--------------

4 2

So the slope is 2/4 or 1/2 after reducing.

The point-slope form a line is

`y-y_1=m(x-x_1)` with a point on the line
`(x_1,y_1)=(1,3)` given and with slope
`m=(1)/(2)` given.

`y-3=(1)/(2)(x-1)`

We are going to solve this for y and simplify what we can because our goal is y=mx+b; this is slope-intercept form. It is called that because it tells us the slope,m, and the y-intercept,b.

Distribute:

`y-3=(1)/(2)x-(1)/(2)`

Add 3 on both sides:

`y=(1)/(2)x-(1)/(2)+3`

Simplify:

`y=(1)/(2)x+(5)/(2)`