Question

Write an equation of each line that passes through the following points in slope-intercept form:

A (8, –1) and B (–4, 17)

Answer 1

`\large\boxed{y=-(3)/(2)x+11}`

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 point A(8, -1) and B(-4, 17). Substitute:

`m=(17-(-1))/(-4-8)=(18)/(-12)=-(3)/(2)`

The equation of a line:

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

Put the coordinates of the point A(8, -1) to the equation of a line:

`-1=-(3)/(2)(8)+b`

`-1=-3(4)+b`

`-1=-12+b` add 12 to both sides

`11=b\to b=11`

Finally we have the equation of a line in a slope-intercept form:

`y=-(3)/(2)x+11`