Final answer:
The value of y for the line with a slope of 1/4 through (-5, -1) and (7, y) is 2.
Step-by-step explanation:
To find the value of y for the line with a slope of 1/4 through (-5, -1) and (7, y), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
First, we find the slope by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) is (-5, -1) and (x2, y2) is (7, y). Plugging in the values, we have (y - (-1)) / (7 - (-5)) = 1/4.
Simplifying the equation, we get (y + 1) / 12 = 1/4. Cross-multiplying, we have 4(y + 1) = 12. Expanding the equation, we get 4y + 4 = 12. Subtracting 4 from both sides, we have 4y = 8. Finally, dividing both sides by 4, we get y = 2.