Given (2, 9) and (3, 2), find the slope.
Understand the Problem
The question is asking to calculate the slope between two given points (2, 9) and (3, 2). The slope can be found using the formula: (y2 - y1) / (x2 - x1).
Answer
The slope is $-7$.
Answer for screen readers
The slope between the points $(2, 9)$ and $(3, 2)$ is $-7$.
Steps to Solve
-
Identify the points
The points given are $(2, 9)$ and $(3, 2)$.
Let $(x_1, y_1) = (2, 9)$ and $(x_2, y_2) = (3, 2)$. -
Use the slope formula
The formula for the slope $m$ is given by:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ -
Substitute the values
Now substitute the coordinates into the formula:
$$ m = \frac{2 - 9}{3 - 2} $$ -
Calculate the difference in y
This gives:
$$ 2 - 9 = -7 $$ -
Calculate the difference in x
This simplifies to:
$$ 3 - 2 = 1 $$ -
Compute the slope
Now we can compute the slope:
$$ m = \frac{-7}{1} = -7 $$
The slope between the points $(2, 9)$ and $(3, 2)$ is $-7$.
More Information
The slope indicates the steepness of the line connecting the two points. A negative slope means that as you move from left to right, the line descends.
Tips
- Forgetting to subtract the $y$ values in the correct order (it should be $y_2 - y_1$, not the other way around).
- Confusing the $x$ values when substituting into the slope formula.
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