Final answer:
The missing y value for the linear function with points (-8, -2) and (3, y) and a slope of -5/2 is -29.5.
Step-by-step explanation:
To find the missing y value of a linear function that passes through the points (-8, -2) and (3, y), with a slope of -5/2, we use the slope formula. The slope, m, can be written as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Plugging in our known values:
m = (y - (-2)) / (3 - (-8))
m = (y + 2) / 11
We know that m = -5/2, so:
-5/2 = (y + 2) / 11
Multiplying both sides by 11 to solve for y:
-5/2 * 11 = y + 2
-27.5 = y + 2
Finally, solving for y:
y = -27.5 - 2
y = -29.5
Therefore, the missing y value is -29.5.