Question

Write the equation of the line that passes through the points (8, -1) and (2,-5) in standard form, giver

slope form is y+1 = (x-8)

Answer 1

2x - 3y = 19

Explanation:

The formula of a slope:

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

We have the points (8, -1) and (2, -5). Substitute:

`m=(-5-(-1))/(2-8)=(-4)/(-6)=(2)/(3)`

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

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

Substitute:

`y-(-1)=(2)/(3)(x-8)`

`y+1=(2)/(3)(x-8)` → the point-slope form

Convert to the standard form:
`Ax+By=C`

`y+1=(2)/(3)(x-8)` multiply both sides by 3

`3y+3=2(x-8)` use the distributive property a(b+c) = ab+ ac

`3y+3=2x-16` subtract 3 from both sides

`3y=2x-19` subreact 2x from both sides

`-2x+3y=-19` change the signs

`2x-3y=19` → the standard form