The points (-4, r) and (2, 1) lie on a line with slope -4. Find the missing coordinate r.
Understand the Problem
The question is asking to find the missing y-coordinate (r) of the point (-4, r), given that the points (-4, r) and (2, 1) lie on a line with a slope of -4. We will use the slope formula to solve for r.
Answer
The missing coordinate \( r \) is $25$.
Answer for screen readers
The missing coordinate ( r ) is $25$.
Steps to Solve
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Identify the points and slope
We have the points ((-4, r)) and ((2, 1)) and the slope (m = -4). -
Use the slope formula
The slope (m) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ For our points, this becomes: $$ -4 = \frac{1 - r}{2 - (-4)} $$ -
Simplify the equation
The denominator simplifies to: $$ 2 - (-4) = 2 + 4 = 6 $$ So we rewrite the slope equation: $$ -4 = \frac{1 - r}{6} $$ -
Clear the fraction
Multiply both sides by 6: $$ -4 \cdot 6 = 1 - r $$
This results in: $$ -24 = 1 - r $$ -
Solve for (r)
Rearranging the equation gives: $$ -24 - 1 = -r $$ $$ -25 = -r $$
Thus, $$ r = 25 $$
The missing coordinate ( r ) is $25$.
More Information
This problem illustrates how to find the missing coordinate of a point on a line using the slope. Knowing the coordinates and slope allows you to set up an equation and solve for the unknown.
Tips
- Forgetting to properly simplify the slope formula can lead to incorrect values for (r).
- Not paying attention to signs when rearranging terms can lead to mistakes in the final answer.
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