Final answer:
The original equation 7x + 8y = -40 has a slope of -7/8. A parallel line will have the same slope. Thus, the equation of the line parallel to the given one and passing through the point (16, -12) is y = (-7/8)x + 2.
Step-by-step explanation:
To write a linear equation that is parallel to the given equation and passes through the point (16,-12), it's important to first note that parallel lines have the same slope. The equation provided is 7x + 8y = -40. We can find the slope by rearranging this into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Rearranging the given equation gives us:
- 8y = -7x - 40
- y = (-7/8)x - 5
The slope of the parallel line will also be -7/8. Now, using the point (16, -12) which the new line must pass through, we can find the y-intercept of our new line by plugging in the x and y values:
y = (-7/8)x + b
-12 = (-7/8)(16) + b
-12 = -14 + b
b = -12 + 14
b = 2
So our new equation, which has the same slope as the original and passes through the point (16,-12), is:
y = (-7/8)x + 2