Question

A line is drawn through (-7, 11) and (8, -9). The equation y - 11 = -4/3(x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.

a) y = -4/3x + 5/3
b) 3y = -4x + 40
c) 4x + y = 21
d) -4x + 3y = 17

Answer 1

The equation y - 11 = -4/3(x + 7) represents a line, and the equation y = -4/3x + 5/3 also represents the same line.

Step-by-step explanation:

The equation y - 11 = -4/3(x + 7) is written in point-slope form, and it represents the line. To check which other equations also represent the line, we need to rearrange them into slope-intercept form (y = mx + b) and compare their slopes and y-intercepts with the given equation.

a) y = -4/3x + 5/3
The slope of this equation (-4/3) matches the given equation, but the y-intercept (5/3) does not.

b) 3y = -4x + 40
This equation is not in slope-intercept form. By rearranging it, we get y = (-4/3)x + 40/3. Both the slope and y-intercept do not match the given equation.

c) 4x + y = 21
By rearranging this equation, we get y = -4x + 21. The slope (-4) matches the given equation, but the y-intercept (21) does not.

d) -4x + 3y = 17
Similar to the previous equation, by rearranging it we get y = (4/3)x + 17/3. Both the slope and y-intercept do not match the given equation.

Therefore, the only equation that represents the line is a) y = -4/3x + 5/3.