Question

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

Answer 1

Answer:

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

Step-by-step 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