Question

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

Answer 1

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

Explanation:

The slope-intercept form of the line equation

`y = mx+b`

where

• m is the slope

• b is the y-intercept

Given the line

`x + 2y = -2`

writing into the slope-intercept form

`2y = - x - 2`

dividing both sides by 2

`y=-(1)/(2)x-1`

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