Question

What is the equation of the line parallel to y=31x+67 that passes through the point (-6, 5)?

A. y−5=31(x+6)
B. y−5=−31(x+6)
C. y+5=31(x+6)
D. y+5=−31(x+6)

Answer 1

The correct answer is A: y-5=31(x+6). This equation is found using the point-slope form with the slope of 31 (same as the given line) and the point (-6, 5) through which the new line must pass.

Step-by-step explanation:

The question asks to find the equation of a line that is parallel to the given equation y=31x+67 and passes through the point (-6, 5). Two lines are parallel if they have the same slope. Since the given equation has a slope of 31, the slope of the required line will also be 31.

We can use the point-slope form of the equation of a line to find the equation of the line parallel to y=31x+67 and passing through point (-6, 5). The point-slope form is given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point the line passes through.

By substituting the slope m=31, and the point (-6,5), we get:

y - 5 = 31(x + 6)

This matches with option A: y - 5 = 31(x + 6), which is the correct answer.