Question

Given (5,-12) is a point on the following line, convert the equation to point-slope form.
6x+ 2y = 6
A. y - 12 = -6(x - 5)
B. y + 12 = -6( – 5)
C. y + 12 = -3(x – 5)
D. y - 12 = -3(x - 5)

Answer 1

Answer:

C

Step-by-step explanation:

Slope = - 3

y - (-12) = -3(x - 5)

y + 12 = -3(x-5)

Answer 2

Answer:

C. y + 12 = -3(x – 5)

Step-by-step explanation:

The point-slope form is

$y-y_{1}=m(x-x_{1})$

To express a line in the point-slope form, we actually its slope and a point that the line crosses. According to the problem, the point is $(5,-12)$.

The slope we can find it from the expression that gives us the problem

$6x+2y=6$

We are gonna express this equation in an explicit form, which is gonna give us the slope. Remember that in explicit form, the slope is the coefficient of the x-variable.

$2y=6-6x\\y=\frac{6-6x}{2}\\ y=3-3x$

As you can observe, the slope is -3.

Now, using all this information, we can find the point-slope expression

$y-y_{1}=m(x-x_{1})\\y-(-12)=-3(x-5)\\y+12=-3(x-5)$

If we compare, we deduct that the correct answer is C., because is the same expression that we have.