Question

Which point lies on the line with a slope of m=2/3 that passes through the point (-3,-2)?

A. (3,4)
B. (5,7)
C. (-8,-4)
D. (-9,-6)

Answer 1

The point that lies on the line with a slope of 2/3 that passes through the point (-3,-2) is (-9,-6). So the correct option is D.

Step-by-step explanation:

To find a point on the line with a slope of 2/3 that passes through the point (-3,-2), we can use the point-slope form of a linear equation. The equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the given values, we have y - (-2) = (2/3)(x - (-3)). Simplifying the equation, we get y + 2 = (2/3)(x + 3).

Now, we can substitute the x-coordinate of each answer option into the equation and solve for y. The point that satisfies the equation will be the point that lies on the line. Let's go through the options:

1. Using (3,4) in the equation, we get 4 + 2 = (2/3)(3 + 3), which simplifies to 6 = 12, which is not true. Therefore, (3,4) does not lie on the line.
2. Using (5,7) in the equation, we get 7 + 2 = (2/3)(5 + 3), which simplifies to 9 = 16/3, which is not true. Therefore, (5,7) does not lie on the line.
3. Using (-8,-4) in the equation, we get -4 + 2 = (2/3)(-8 + 3), which simplifies to -2 = -10/3, which is not true. Therefore, (-8,-4) does not lie on the line.
4. Using (-9,-6) in the equation, we get -6 + 2 = (2/3)(-9 + 3), which simplifies to -4 = -12/3, which is true. Therefore, (-9,-6) lies on the line.

So, the point that lies on the line with a slope of 2/3 that passes through the point (-3,-2) is D. (-9,-6).

Answer 2

D. (-9,-6)

Step-by-step explanation:

Use the given slope and point to solve for y using the point-slope equation.

y-y = m(x - x)

m= 2/3 (-3, -2)

y + 2 = 2/3(x + 3)

y + 2 = 2/3x + 2

y = 2/3x

Then plug in the x's in the points that you can choose from. If the y equals the y in the given point that is the answer.

( 3,4) y = 2/3(3) = 2

( 5,7) y = 2/3(5) = 10/3

( -8, -4) y = 2/3(-8) = - 16/3

( -9, -6) y = 2/3(-9) = -6