Question

Line MN passes through points M4, 3) and M7, 12). If the equation of the line is written in slope-intercept form, y-mx+ b, what is the value of b?

Answer 1

b = -9

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points M(4, 3) and N(7, 12). Substitute:

`m=(12-3)/(7-4)=(9)/(3)=3`

Therefore we have the equation:

`y=3x+b`

Put the coordinates of the point M to the equation:

`3=3(4)+b`

`3=12+b` subtract 12 from both sides

`-9=b`