Question

Find the equation of the line that passes through the following two points:

(5, 7) and (1, 10)

Answer 1

Answer: y=-3/4x+43/4

Explanation:

y = mx+b

m is the slope, and

b is the y-intercept

m= y2-y1 / x2-x1

m= 10-7/ 1-5

m=-3/4

Answer 2

Answer: y =
`-(3)/(4)`x + 10
`(3)/(4)`

Explanation:

If we know the two points, we can find the slope and write a point-slope equation.

Slope

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) )=(10-7)/(1-5) =(3)/(-4) =(-3)/(4)`

Point-slope equation

y -
`y_1` = m(x -
`x_1`)

y - 7 =
`-(3)/(4)`(x - 5)

y - 7 =
`-(3)/(4)`x + 3
`(3)/(4)`

y =
`-(3)/(4)`x + 10
`(3)/(4)`

Slope-intercept form equation

y =
`-(3)/(4)`x + 10
`(3)/(4)`