Question

Which choices are equations for the line shown below? Check all that apply.(-2,5)(2-3)A. y + 3 = -2(x - 2)B. y-5=-2(x + 2)C. y = 2x+1D. y=-0.5x + 1Ey- 5 = -2(x - 2)

Answer 1

Given the points on the line:

(x1, y1) ==> (-2, 5)

(x2, y2) ==> (2, -3)

Let's find the equations that represent the line.

Apply the point-slope form:

y - y1 = m(x - x1)

Where m represents the slope, x1 and y1 represents the values of one point on the line.

To find the slope of the line apply the slope formula:

`m=(y2-y1)/(x2-x1)`

Substitute values into the formula and solve for m:

`\begin{gathered} m=(-3-5)/(2-(-2)) \\ \\ m=(-3-5)/(2+2) \\ \\ m=(-8)/(4) \\ \\ m=-2 \end{gathered}`

Substitute -2 for m in the point-slope equation:

y - y1 = -2(x - x1)

Substitute the coordinates of each point for x1 and y1

At (-2, 5):

y - 5 = -2(x - (-2)) ==> y - 5 = -2(x + 2)

At (2, -3):

y - (-3) = -2(x - 2) ==> y + 3 = -2(x - 2)

The possible equations for line are:

• y - 5 = -2(x + 2)

• y + 3 = -2(x - 2)

ANSWER:

• A. y + 3= -2(x - 2)

• B. y - 5 = -2(x + 2)