Algebra-1

To determine which line goes through the point (0, -2) and is parallel to y = 5x + 7, we need to compare the slopes of the given lines.

The slope of the line y = 5x + 7 is 5. Any line parallel to this line will also have a slope of 5.

Now let's analyze the options:

A. y = 5x - 2
The slope of this line is 5, which is equal to the slope of y = 5x + 7. However, when x = 0, y = -2, which satisfies the point (0, -2). Therefore, line A is parallel to y = 5x + 7 and passes through (0, -2).

B. y = -2x + 7
The slope of this line is -2, which is not equal to 5. Therefore, line B is not parallel to y = 5x + 7.

C. y = 5(x - 2)
This equation represents a line with a slope of 5, which is equal to the slope of y = 5x + 7. However, when x = 0, y = 5(-2) = -10, which does not satisfy the point (0, -2). Therefore, line C is parallel to y = 5x + 7 but does not pass through (0, -2).

D.

Click "Show Answer" to reveal the answer and analysis