Question

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

Answer 1

Answer:

$y=\frac{1}{2}x+\frac{5}{2}$

Step-by-step 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 $\frac{y_2-y_1}{x_2-x_1}$.  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 $m=\frac{1}{2}$ given.

$y-3=\frac{1}{2}(x-1)$

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:

$y-3=\frac{1}{2}x-\frac{1}{2}$

Add 3 on both sides:

$y=\frac{1}{2}x-\frac{1}{2}+3$

Simplify:

$y=\frac{1}{2}x+\frac{5}{2}$