What is the slope of the line that passes through the points (2, -5) and (-3, y)?
Understand the Problem
The question is asking us to find the slope of a line that passes through two points, (2, -5) and (-3, y). To solve for the slope, we use the slope formula which is (y2 - y1) / (x2 - x1) where (x1, y1) = (2, -5) and (x2, y2) = (-3, y).
Answer
\( y = -5 \cdot \text{known value} - 5 \)
Answer for screen readers
The value of ( y ) will depend on the specified known slope value you use.
Steps to Solve
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Identify Coordinates The first step is to identify the coordinates of the points given. We have point 1 $(x_1, y_1) = (2, -5)$ and point 2 $(x_2, y_2) = (-3, y)$.
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Substitute into the Slope Formula The slope (m) is calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Substitute the coordinates into the formula: $$ m = \frac{y - (-5)}{-3 - 2} $$ This simplifies to: $$ m = \frac{y + 5}{-5} $$
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Simplify the Slope Expression From the equation we found: $$ m = \frac{y + 5}{-5} $$ This represents the slope in terms of y.
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Set the Slope Equal to a Known Value If π (3.14) is known as a specific slope we want to work with, set the slope equation equal to that known value and solve for y: $$ \frac{y + 5}{-5} = \text{known value} $$
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Solve for y Multiply both sides by -5: $$ y + 5 = -5 \cdot \text{known value} $$ Then isolate y: $$ y = -5 \cdot \text{known value} - 5 $$
The value of ( y ) will depend on the specified known slope value you use.
More Information
When finding the slope of a line through two points, the slope tells you how steep the line is. The value of y can vary depending on your specific slope input.
Tips
- Forgetting to subtract the y-coordinates in the correct order. Remember, it should be $y_2 - y_1$.
- Miscalculating the $(x_2 - x_1)$ term, potentially leading to incorrect signs in the slope.
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