Question

Write the equation of the line that passes
through the point (3, -3) and has a slope of -2.

Answer 1

Explanation:

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

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

m - slope

(x₁, y₁) - point on a line

We have the point (3, -3) and the slope m = -2. Substitute:

`y-(-3)=-2(x-3)`

`y+3=-2(x-3)` - point-slope form

Convert to the slope-intercept form (y = mx + b):

`y+3=-2(x-3)` use the distributtive property

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

`y+3=-2x+6` subtract 3 from both sides

`y=-2x+3` - slope-intercept form

Convert to the standard form (Ax + By = C):

`y=-2x+3` add 2x to both sides

`2x+y=3` - standard form

Convert to the general form (Ax + By + C = 0):

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

`2x+y-3=0` - general form