Answer:
[tex]y=\frac{2}{3}x+6[/tex]
Step-by-step explanation:
step 1
Find the midpoint of (5,6) and (1,10)
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M(\frac{5+1}{2},\frac{6+10}{2})[/tex]
[tex]M(3,8)[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex] ----> the gradient is the same that the slope
[tex]point\ (3,8)[/tex]
substitute
[tex]y-8=\frac{2}{3}(x-3)[/tex]
Convert to slope intercept form
isolate the variable y
[tex]y-8=\frac{2}{3}x-2[/tex]
[tex]y=\frac{2}{3}x-2+8[/tex]
[tex]y=\frac{2}{3}x+6[/tex]
