Answer: A line that is parallel to another line has the same slope. The slope of the line x-2y=6 can be found by rearranging it into slope-intercept form, y = mx + b, where m is the slope:
x - 2y = 6
Add 2y to both sides:
x = 2y + 6
Divide both sides by 2:
y = (1/2)x + 3
So the slope of the line x - 2y = 6 is m = 1/2.
Since the line through the point (−6,−8) must have the same slope as the line x-2y=6, its slope is also 1/2. To find the equation of this line, we can use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope. Substituting the values m = 1/2, x1 = -6, and y1 = -8 into the point-slope form gives:
y - (-8) = (1/2)(x - (-6))
Expanding the right side:
y + 8 = (1/2)x + (1/2)(-6)
y + 8 = (1/2)x - 3
Multiplying both sides by 2:
2y + 16 = x - 6
Adding 6 to both sides:
2y + 22 = x
So the equation of the line that passes through the point (−6,−8) and is parallel to the line x - 2y = 6 is:
2y + 22 = x
Explanation: