A line is parallel to x + 2y = -2 and intersects the point (6, 9). What is the equation of this parallel line?

The equation of the parallel line is: y = -1/2x + 12

Step-by-step explanation:

The slope-intercept form of the line equation

where

Given the line

writing into the slope-intercept form

dividing both sides by 2

comparing with the slope-intercept form y = mx+b

Thus, the slope m of the equation is: m = -1/2

We know that the parallel lines have the same slope.

Thus, the slope of a new line parallel to x + 2y = -2 is also: -1/2

Given that the line intersects the point (6, 9).

so substituting m = -1/2 and (6, 9) in the slope-intercept form to determine the y-intercept

y = mx+b

9 = -1/2(6) + b

9 = -3 + b

b = 9+3

b = 12

Thus, the y-intercept b = 12

now substituting b = 12 and m = -1/2 in the slope-intercept

y = mx+b

y = -1/2x + 12

Therefore, the equation of the parallel line is: y = -1/2x + 12

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step-by-step explanation: