Question

What is the equation of the line slope of 3 and passes through the point (-2, 3)?

Answer 1

`\large\boxed{y-3=3(x+2)}\qquad\text{point-slope form}\\\boxed{y=3x+9}\qquad\text{slope-intercept form}\\\boxed{3x-y=-9}\qquad\text{standard form}\\\boxed{3x-y+9=0}\qquad\text{general form}`

Explanation:

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

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

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

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

the point-slope form

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

`y-3=3x+6` add 3 to both sides

`y=3x+9`

the slope-intercept form

`y=3x+9` subtract 3x from both sides

`-3x+y=9` change the signs

`3x-y=-9`

the standard form

`3x-y=-9` add 9 to both sides

`3x-y+9=0`

the general form