Which of the following equations represents the line that is parallel to the line y=5x+2 and that passes through the point (1,-3)?

To find the equation of a line that is parallel to the line y = 5x + 2 and passes through the point (1, -3), we need to use the fact that parallel lines have the same slope.

The given line has a slope of 5 (the coefficient of x).

Since the line we're looking for is parallel, it will also have a slope of 5.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute (1, -3) as (x1, y1) and 5 as the slope:

y - (-3) = 5(x - 1)
y + 3 = 5x - 5

Next, simplify the equation:

y = 5x - 5 - 3
y = 5x - 8

Therefore, the equation of the line that is parallel to y = 5x + 2 and passes through the point (1, -3) is y = 5x - 8.

To determine the equation of a line parallel to the line y=5x+2 and passing through the point (1, -3), we need to use the fact that parallel lines have the same slope.

First, we can determine the slope of the given line. The equation y=5x+2 is in the form y=mx+b, where m represents the slope. In this case, m=5.

Since the line we want to find is parallel, it will also have a slope of 5.

We can now use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values into the point-slope form, we get:
y - (-3) = 5(x - 1)

Simplifying the equation:
y + 3 = 5x - 5

To obtain the final form y = mx + b, rearrange the equation:
y = 5x - 8

Therefore, the equation of the line parallel to y=5x+2 and passing through the point (1, -3) is y = 5x - 8.

You know that y=5x+2 has slope 5. Now just use the point-slope form of the line:

y+3 = 5(x-1)

You can massage that into one of your choices, if it's not already there.