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

Answer:

2x - 3y = 19

Step-by-step explanation:

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{-5-(-1)}{2-8}=\dfrac{-4}{-6}=\dfrac{2}{3}$

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

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

Substitute:

$y-(-1)=\dfrac{2}{3}(x-8)$

$y+1=\dfrac{2}{3}(x-8)$ → the point-slope form

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

$y+1=\dfrac{2}{3}(x-8)$        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