Given the table below, find the slope.
Understand the Problem
The question is asking to calculate the slope based on the given values of x and y from the table. The slope can be determined using the formula (y2 - y1) / (x2 - x1) using the two points provided.
Answer
The slope is \( m = -8 \).
Answer for screen readers
The slope is ( m = -8 ).
Steps to Solve
- Identify the points from the table
From the table, we have two points:
- Point 1: $(x_1, y_1) = (8, -4)$
- Point 2: $(x_2, y_2) = (7, 4)$
- Apply the slope formula
The slope $m$ is calculated using the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Substituting the values:
$$ m = \frac{4 - (-4)}{7 - 8} $$
- Calculate the difference in y-coordinates
Calculate $y_2 - y_1$:
$$ y_2 - y_1 = 4 - (-4) = 4 + 4 = 8 $$
- Calculate the difference in x-coordinates
Calculate $x_2 - x_1$:
$$ x_2 - x_1 = 7 - 8 = -1 $$
- Calculate the slope
Substituting these differences into the slope formula gives:
$$ m = \frac{8}{-1} = -8 $$
The slope is ( m = -8 ).
More Information
The slope represents the rate of change between the two points. A negative slope indicates that as ( x ) increases, ( y ) decreases.
Tips
- Confusing the order of the points: Remember that the first point should be ((x_1, y_1)) and the second ((x_2, y_2)).
- Not considering the subtraction of a negative when calculating (y_2 - y_1).
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