Question

"A line is drawn through (-7, 11) and (8, -9). The equation -11 = (r+7) is written to represent the line. Which equations also represent the line? Check all that apply.

A) y = -4x + 5
B) 3y = 4x + 40
C) 4x + y = 21
D) 4x + 3y = 5"

Answer 1

To determine which equations represent the line passing through (-7, 11) and (8, -9), we can find the slope of the line and check if it matches the given equations. Equations B and D represent the line.

Step-by-step explanation:

To determine which equations represent the line passing through (-7, 11) and (8, -9), we can find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates, we get m = (-9 - 11) / (8 - (-7)) = -20 / 15 = -4/3. So, any equation with a slope of -4/3 will represent the line.

Let's check each option:

A) y = -4x + 5: The slope of this equation is -4, not -4/3, so it does not represent the line.

B) 3y = 4x + 40: Dividing by 3, we get y = (4/3)x + 40/3, which has a slope of 4/3. Therefore, this equation represents the line.

C) 4x + y = 21: Rearranging, we get y = -4x + 21. Again, the slope is -4, not -4/3, so this equation does not represent the line.

D) 4x + 3y = 5: Dividing by 3, we get y = (-4/3)x + 5/3, which has a slope of -4/3. Therefore, this equation represents the line.

Based on the calculations, equations B and D represent the given line.