Answer: To find the equation of a line parallel to 12x + 8y = -40, we need to first rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
12x + 8y = -40
8y = -12x - 40
y = -1.5x - 5
So, the slope of the line is -1.5.
Since the line we want is parallel to this line, it will have the same slope, which is -1.5. Now we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes, and m is the slope.
Substituting (6,-3) and -1.5 for x1, y1, and m respectively, we get:
y - (-3) = -1.5(x - 6)
y + 3 = -1.5x + 9
y = -1.5x + 6
So the equation of the line parallel to 12x + 8y = -40 through the point (6,-3) is y = -1.5x + 6.
Explanation: