Question

Write an equation for the line that is parallel to the given line and that passes through the given point. y = –5x + 3; (–6, 3)

A) y = –5x – 27
B) y = –5x + 27
C) y = 5x – 9
D) y = –5x + 9

Answer 1

The correct equation for a line parallel to y = -5x + 3 that goes through the point (-6, 3) is y = -5x - 27, which is option A.

Step-by-step explanation:

The student has asked us to write an equation for a line that is parallel to the given line y = –5x + 3 and passes through the point (–6, 3). Lines that are parallel to each other have the same slope (m). The slope of the given line is –5. To find the equation of the parallel line, we keep the same slope and use the point given to find the y-intercept (b).

Using the point-slope form of a line equation:
y – y1 = m(x – x1), where (x1, y1) are the coordinates of the given point and m is the slope, we substitute the values to get:
y – 3 = –5(x + 6).
Solving this we get the equation y = –5x – 30 + 3, which simplifies to y = –5x – 27.
Therefore, the correct option is A) y = –5x – 27.