Question

The equation of a line is y-4=3(x+2), which of the following is a point on the line

A) (2,4)
B) (4,-2)
C) (-2,4)
D (-4,2)

Answer 1

y - 4 = 3(x + 2)

This equation is in point-slope form, which is y - b = m(x - a), where m is the slope and (a, b) is a point on the line.

An equation in point-slope form contains the negated forms of the coordinates on its graph. Here we have negative 4 and positive 2. This means the original coordinate contains positive 4 and negative 2. Remember, b is -4 and a is 2, so the point on the line is (-2, 4).

Let's check this by plugging in the coordinate.

y - b = m(x - a)

y - (4) = m(x - (-2))

y - 4 = m(x + 2) -- These are the same signs as the point-slope equation

Answer:

C) (-2, 4)

Answer 2

Remark

The easiest way to do this would be to substitute all values into the given equation. The best way is probably to translate the equation into the slope form equation.

Since you may not know the slope y intercept form, I'll just do it by substitution into the give equation. The left and right sides should be equal.

Solution.

y - 4 = 3(x + 2) use 2,4

4 - 4 = 3(2 + 1)

0 <> 12 So A is not the answer.

y - 4 = 3(x + 2) use 4,-2

-2 - 4 =3(4 +2)

- 6 = 18 B is not the answer.

y - 4 = 3(x + 2) use -2,4

4 - 4 = 3(-2 + 2) Here we are.

0 = 3*0

0 = 0

y - 4 = 3(x + 2) use -4,2

2 - 4 = 3(-4 + 2)

-2 = -6 which is not true so D does not work.