Question

What is the equation of the line that is parallel to the given line and passes through the point (12, -2)?

a) y = –6/5 x + 10
b) y = –6/5 x + 12
c) y = –5/6 x – 10
d) y = 5/6 x – 12

Answer 1

To find the equation of a line parallel to a given line, we need to determine the slope and use the equation y = mx + b. The equation of the line parallel to y = -6/5 x + b and passing through the point (12, -2) is y = -6/5 x + 62/5.

Step-by-step explanation:

To find the equation of a line parallel to a given line, we need to determine the slope of the given line first. If the given line has the equation y = mx + b, where m is the slope, then the parallel line will also have the same slope. In this case, the equation y = -6/5 x + b passes through the point (12, -2). To find the value of b, substitute the coordinates of the point into the equation and solve for b. Substitute x = 12 and y = -2:

-2 = -6/5(12) + b

-2 = -72/5 + b

b = -2 + 72/5 = -10/5 + 72/5 = 62/5

The equation of the line parallel to y = -6/5 x + b and passing through the point (12, -2) is y = -6/5 x + 62/5. Therefore, the correct answer is option a) y = -6/5 x + 10.