The value of z on the line with a slope of -1/4 passing through points (4, -2) and (z, 1) is -8.
To find the value of z for the line that includes the points (4,–2) and (z,1) with a slope of –1/4, we can use the formula for the slope of a line between two points: slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (4, -2) and (x2, y2) = (z, 1). Plugging in the given values and the slope, we have:
-1/4 = (1 - (-2)) / (z - 4)
-1/4 = 3 / (z - 4)
To solve for z, we'll cross-multiply and then simplify the equation:
-1 * (z - 4) = 4 * 3
- z + 4 = 12
-z = 12 - 4
-z = 8
z = -8
Therefore, the value of z is -8.