Question

For the equation y - 3 = 2(x + 4), which of the following is true?

A. The line has a slope of 2 and passes through the point (3, -4).
B. The line has a slope of 2 and passes through the point (-3, 4).
C. The line has a slope of 2 and passes through the point (-4, 3).
D. The line has a slope of 2 and passes through the point (4, -3).

Answer 1

The equation y - 3 = 2(x + 4) has a slope of 2 and passes through the points (3, -4), (-3, 4), and (-4, 3).

Step-by-step explanation:

The equation y - 3 = 2(x + 4) is in the form y = mx + b, where m represents the slope and b represents the y-intercept. Comparing it with the given equation, we can determine that the slope is 2 and the y-intercept is -3.

To verify which option is correct, we can substitute the coordinates of each point into the equation and see if the equation holds true.

1. Option A: Substituting (3, -4) into the equation gives -4 - 3 = 2(3 + 4), which is true.
2. Option B: Substituting (-3, 4) into the equation gives 4 - 3 = 2(-3 + 4), which is true.
3. Option C: Substituting (-4, 3) into the equation gives 3 - 3 = 2(-4 + 4), which is true.
4. Option D: Substituting (4, -3) into the equation gives -3 - 3 = 2(4 + 4), which is false.

Based on the calculations, we can conclude that option A, B, and C are all true. Therefore, the correct answer is options A, B, and C.