Final answer:
To find the value of y that will make the points (-4, 6) and (2, y) lie on a line with slope 3, we use the slope formula and solve for y, which gives us y = 24.
Step-by-step explanation:
To find the value of y so that the points (-4, 6) and (2, y) lie on a line with a given slope, we can use the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1)
We're given the slope and one point, so we rearrange the formula to solve for y:
y = m(x2 - x1) + y1
Substitute the given values (slope = 3, x1 = -4, y1 = 6, x2 = 2) into the equation:
y = 3(2 - (-4)) + 6
y = 3(6) + 6
y = 18 + 6
y = 24
The value of y that makes the points lie on a line with a slope of 3 is 24.