Question

Which of the following are equations for the line shown below? Check all that apply. O A. y=-3x-3 O B. y+ 5= 3(x- 1) O C. y= 3x-2 O D. y-4 = 3(x+ 2)

Answer 1

B

Explanation:

Answer 2

The equations for the line shown below are B. y + 5 = -3(x - 1) and D. y - 4 = -3(x + 2).

To determine which equations represent the line passing through the points (-2, 4) and (1, -5), we can use the point-slope form of a linear equation:

`\[y - y_1 = m(x - x_1)\]`

where
`\((x_1, y_1)\)` is a point on the line, and \(m\) is the slope.

Given the points (-2, 4) and (1, -5), we can find the slope:

`\[m = (y_2 - y_1)/(x_2 - x_1)\]`

`\[m = (-5 - 4)/(1 - (-2)) = (-9)/(3) = -3\]`

Now, let's use the point-slope form with one of the points:

`\[y - 4 = -3(x + 2)\]`

Now, let's compare this with the given options:

A. y = -3x - 3 - Not equivalent.

B. y + 5 = -3(x - 1) - Equivalent after simplification.

C. y = -3x - 2 - Not equivalent.

D. y - 4 = -3(x + 2) - Equivalent.

So, the correct choices are:

- B. y + 5 = -3(x - 1)

- D. y - 4 = -3(x + 2)