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

`y=(2)/(3)x+6`

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((x1+x2)/(2),(y1+y2)/(2))`

substitute the values

`M((5+1)/(2),(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=(2)/(3)` ----> the gradient is the same that the slope

`point\ (3,8)`

substitute

`y-8=(2)/(3)(x-3)`

Convert to slope intercept form

isolate the variable y

`y-8=(2)/(3)x-2`

`y=(2)/(3)x-2+8`

`y=(2)/(3)x+6`