The pair of points (6, y) and (10, -1) lie on a line with slope 1/4. what is the value of y?
We can use the formula for the slope of a line:
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.
We are given that the slope is \(\frac{1}{4}\), and one point is \((10, -1)\). So, we have:
\[\frac{1}{4} = \frac{y - (-1)}{6 - 10}\]
Simplifying the equation, we get:
\[\frac{1}{4} = \frac{y + 1}{-4}\]
Multiply both sides by -4:
\[-1 = y + 1\]
Subtract 1 from both sides:
\[-2 = y\]
Therefore, the value of \(y\) is -2.