Question

What is an equation of the line that passes through the point (4, - 6) and has a slope of -3

Answer 1

`y=-3x+6`

Explanation:

Use the point-slope formula:

`y-y(1)=m(x-x(1))`

m is the slope. Fill in the values:

`y-(-6)=-3(x-4)`

Simplify parentheses (negative+negative=positive):

`y+6=-3(x-4)`

Solve for y:

Use the distributive property:

`y+6=-3(x)-3(-4)\\y+6=-3x+12`

Subtract 6 from both sides:

`y+6-6=-3x+12-6\\y=-3x+6`

Written in slope-intercept form,
`y=mx+b` , with m as slope and b as the y-intercept, the equation is
`y=-3x+6` .

Done.

Answer 2

Y = -3x + 6

Explanation:

Y = Mx + B

we turn this into

-6 = -3 ( 4 ) + B (-3 is our slope, and X= 4, however we DO NOT know B)

-6 = -12 + B

move the -12 to the other side to isolate B

-6 + 12 = 6

6 = B

there for

Y= -3x + 6 is the answer