Which point is located on the line represented by the equation y + 4 = –5(x – 3)?
A. (–4, –5)
B. (–5, –4)
C. (3, –4)
D. (–3, 4)
To determine which point is located on the line represented by the equation, we need to substitute the coordinates of each point into the equation and check if the equation holds true.
We can start with option A: (-4, -5)
Substituting x = -4 and y = -5 into the equation:
-5 + 4 = -5(-4 - 3)
-1 = -5(-7)
-1 = 35
Since -1 does not equal 35, (-4, -5) is not on the line represented by the equation.
We can move on to the next option: (-5, -4)
Substituting x = -5 and y = -4 into the equation:
-4 + 4 = -5(-5 - 3)
0 = 40
Since 0 does not equal 40, (-5, -4) is not on the line represented by the equation.
Next, let's try option C: (3, -4)
Substituting x = 3 and y = -4 into the equation:
-4 + 4 = -5(3 - 3)
0 = 0
Since 0 equals 0, (3, -4) is on the line represented by the equation.
Finally, let's test option D: (-3, 4)
Substituting x = -3 and y = 4 into the equation:
4 + 4 = -5(-3 - 3)
8 = 30
Since 8 does not equal 30, (-3, 4) is not on the line represented by the equation.
Therefore, the point located on the line represented by the equation y + 4 = –5(x – 3) is C. (3, -4).