Questions: The points (-2, 7) and (14, 2) lie on a line with slope -1/4. Find the missing coordinate: r =

Solution Steps

To find the missing coordinate \( r \) on the line with a given slope, we can use the point-slope form of a line equation. We know two points on the line and the slope, so we can set up the equation using one of the points and solve for the missing coordinate.

We are given two points on a line: \( (-2, 7) \) and \( (14, 2) \), along with the slope of the line, which is \( m = -\frac{1}{4} \).

The slope \( m \) of a line can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the points into the formula, we have: \[ -\frac{1}{4} = \frac{2 - 7}{14 - (-2)} \]

To find the missing coordinate \( r \), we can rearrange the slope formula. We can express \( r \) in terms of the known coordinates: \[ r = x_1 + \frac{y_2 - y_1}{m} \] Substituting the values: \[ r = -2 + \frac{2 - 7}{-\frac{1}{4}} = -2 + \frac{-5}{-\frac{1}{4}} = -2 + 20 = 18 \]

Final Answer