# slope?

#### ESHA_221

##### New member
what is an equation of the line that passes through the point (4,-6) and has a slope of -3?

a) y=-3x+6
b) y=-3x-6
c) y=-3x+10
d) y=-3x+14

i dont get this question at all.

#### mertz

##### New member
m = -3
y = mx + b
y =-3x + b
To solve SUBSTITUTE the point (4,-6), where x=4, y=-6and SOLVE for b
y = -3x + b
-6= -3(4) + b
-6= -12 + b ADD 12 to both sides
6= b

The y-intercept is 6

CHECK
The equation for the line in the form y = mx + b is:
y = -3x + 6
SUBSTITUTE the point (4, -6)
-6 = -3(4) + 6
- 6 = -12 + 6
-6 = -6 it checks out

#### mmm4444bot

##### Super Moderator
Staff member
Yup.

Another way is to use the Point-Slope form of a line.

This form is useful when you're given the slope and the coordinates of a single point, but not given the y-intercept.

y - y[sub:2l5k7fis]1[/sub:2l5k7fis] = m(x - x[sub:2l5k7fis]1[/sub:2l5k7fis])

You know that m = -3 and that (x[sub:2l5k7fis]1[/sub:2l5k7fis], y[sub:2l5k7fis]1[/sub:2l5k7fis]) is (4, -6).

y + 6 = -3(x - 4)

Simplify the righthand side and then solve for y, to get the Slope-Intercept form shown in multiple-choice answer (a).