Answer:
Part 1) [tex]y-5=\frac{1}{2}(x-1)[/tex]
Part 2) [tex]y=\frac{1}{2}x+\frac{9}{2}[/tex] or [tex]y=0.5x+4.5[/tex]
Step-by-step explanation:
we have
(1,5) and (3,6)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{6-5}{3-1}[/tex]
[tex]m=\frac{1}{2}[/tex]
Part 1) Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{2}[/tex]
[tex]point\ (1,5)[/tex]
substitute
[tex]y-5=\frac{1}{2}(x-1)[/tex]
Part 2) Find the equation in slope-intercept form
[tex]y=mx+b[/tex]
we have
[tex]y-5=\frac{1}{2}(x-1)[/tex]
isolate the variable y
[tex]y-5=\frac{1}{2}x-\frac{1}{2}\\\\y=\frac{1}{2}x-\frac{1}{2}+5\\\\y=\frac{1}{2}x+\frac{9}{2}[/tex]
