Question

A line with gradient 2/3 passes through the midpoint of (5,6) and (1,10). find the equation of the line ​

Answer 1

Answer:

$y=\frac{2}{3}x+6$

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

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{5+1}{2},\frac{6+10}{2})$

$M(3,8)$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{3}$ ----> the gradient is the same that the slope

$point\ (3,8)$

substitute

$y-8=\frac{2}{3}(x-3)$

Convert to slope intercept form

isolate the variable y

$y-8=\frac{2}{3}x-2$

$y=\frac{2}{3}x-2+8$

$y=\frac{2}{3}x+6$