Answer:
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]
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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. 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
[tex]y-y_1=m(x-x_1)[/tex] with a point on the line [tex](x_1,y_1)=(1,3)[/tex] given and with slope [tex]m=\frac{1}{2}[/tex] given.
[tex]y-3=\frac{1}{2}(x-1)[/tex]
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:
[tex]y-3=\frac{1}{2}x-\frac{1}{2}[/tex]
Add 3 on both sides:
[tex]y=\frac{1}{2}x-\frac{1}{2}+3[/tex]
Simplify:
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]
