Question

Identify an equation for the line PARALLEL to the line y = -x + 4 and passing through the point (3, 9).

a) y = -x + 12
b) y = -x + 6
c) y = x + 6
d) y = x + 12

Answer 1

To find the equation for a line parallel to y = -x + 4 and passing through the point (3, 9), we can use the point-slope form.

Step-by-step explanation:

To find the equation for a line parallel to y = -x + 4 and passing through the point (3, 9), we need to find a line with the same slope as -1 (the coefficient of x) and a different y-intercept. Since the slope is the same, the answer options (a) and (b) can be eliminated since their slopes are different. To find the correct equation, we can use the point-slope form, where m is the slope and (x1, y1) are the coordinates of the given point. Plugging in the values, we get:

y - y1 = m(x - x1)

y - 9 = -1(x - 3)

y - 9 = -x + 3

y = -x + 12

So, the equation for the line parallel to y = -x + 4 and passing through the point (3, 9) is y = -x + 12 (option a)