Final answer:
To find a linear equation parallel to 7x + 8 = -40 passing through (16, -12), first identify the slope of the original line, which is 7. A parallel line will have the same slope. The equation of the parallel line is then found to be y = 7x - 124 by using the point-slope form and simplifying.
Step-by-step explanation:
To write a linear equation that is parallel to 7x + 8 = -40 and passes through the point (16, -12), we first need to identify the slope of the given line. We can rearrange the equation into the slope-intercept form (y = mx + b) to find the slope (m). Starting with the original equation:
7x + 8 = -40
Subtract 8 from both sides:
y = 7x - 48
The slope of the given line is 7 since it is the coefficient of x. A parallel line will have the same slope. Therefore, the parallel line will also have a slope of 7.
Next, we use the point-slope form of a line, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the slope 7 and point (16, -12):
(y - (-12)) = 7(x - 16)
Simplify the equation:
y + 12 = 7x - 112
Subtract 12 from both sides to get the final equation:
y = 7x - 124
The linear equation parallel to 7x + 8 = -40 and passing through the point (16, -12) is y = 7x - 124.