Given the table below, find the slope.

Question image

Understand the Problem

The question is asking to calculate the slope given the values of x and y from the provided table. The slope can be found using the formula (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points from the table.

Answer

The slope is $m = -2$.
Answer for screen readers

The slope is $m = -2$.

Steps to Solve

  1. Identify the Points

The two points from the table are:

  • Point 1: $(x_1, y_1) = (8, 3)$
  • Point 2: $(x_2, y_2) = (7, 5)$
  1. Apply the Slope Formula

Use the slope formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Substituting the values:

$$ m = \frac{5 - 3}{7 - 8} $$

  1. Calculate the Numerator

Calculate the difference in y-values:

$$ m = \frac{2}{7 - 8} $$

  1. Calculate the Denominator

Calculate the difference in x-values:

$$ m = \frac{2}{-1} $$

  1. Find the Slope

Therefore, the slope is:

$$ m = -2 $$

The slope is $m = -2$.

More Information

The slope represents the rate of change of $y$ with respect to $x$. A negative slope indicates that as $x$ increases, $y$ decreases.

Tips

  • Confusing the order of points: Always ensure you correctly assign $(x_1, y_1)$ and $(x_2, y_2)$.
  • Not subtracting in the correct order can lead to an incorrect sign for the slope.
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