Question

Write an equation of the line that passes through each pair of points (-3, -5) and (6, -2)

Answer 1

The point-slope form:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have the points (-3, -5) and (6, -2). Substitute:

`m=(-2-(-5))/(6-(-3))=(-2+5)/(6+3)=(3)/(9)=(1)/(3)\\\\y-(-5)=(1)/(3)(x-(-3))\\\\y+5=(1)/(3)(x+3)\qquad\text{use distributive property}\\\\y+5=(1)/(3)x+1\qquad\text{subtract 5 from both sides}\\\\y=(1)/(3)x-4\qquad\text{multiply both sides by 3}\\\\3y=1x-12\qquad\text{subtract x from both sides}\\\\-x+3y=-12\qquad\text{change the signs}\\\\x-3y=12`

Answer:

point-slope form: y + 5 = 1/3(x + 3)

slope-intercept form: y = 1/3 x + 12

standard form: x - 3y = 12