Question

Find an equation for the line parallel to y = -3x + 6 and goes through the point (3, 5). Write your answer in the form y = mx + b.

a) y = -3x + 14
b) y = -3x - 4
c) y = -3x + 5
d) y = -3x - 6

Answer 1

The equation for a line parallel to y = -3x + 6 that goes through the point (3, 5) is y = -3x + 14.

Step-by-step explanation:

The student is asking to find an equation for a line that is parallel to the given line y = -3x + 6 and that passes through the point (3, 5). Parallel lines have the same slope, so the slope of the new line will also be -3.

To find the y-intercept (b) of the new line, we use the point-slope form:

y - y1 = m(x - x1)

Plugging in the point (3, 5), we get:

5 - (-3)(3) = 5 + 9 = 14

Thus, the equation of the new line is y = -3x + 14.

All other options do not satisfy the condition that the line must go through the point (3, 5).