Given the table below, find the slope.

Question image

Understand the Problem

The question is asking to find the slope between two points given in the table, where x and y coordinates are provided. The slope can be calculated using the formula (y2 - y1) / (x2 - x1).

Answer

The slope is $-1$.
Answer for screen readers

The slope between the two points is $-1$.

Steps to Solve

  1. Identify the Points

From the table, the points are:

  • Point 1: $(x_1, y_1) = (8, 0)$
  • Point 2: $(x_2, y_2) = (7, 1)$
  1. Use the Slope Formula

The slope $m$ between two points is calculated using the formula:

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

Substituting the values of the points into the formula:

$$ m = \frac{1 - 0}{7 - 8} $$

  1. Calculate the Slope

Now perform the calculations:

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

  1. Final Result

Calculating the above gives:

$$ m = -1 $$

The slope between the two points is $-1$.

More Information

The slope represents the rate of change between the two points and indicates that for each unit increase in the x-direction, the y-value decreases by 1 unit.

Tips

  • Mixing up the coordinates: Always double-check that $x_1$ and $y_1$ correspond to the same point, as well as $x_2$ and $y_2$.
  • Forgetting to subtract in the correct order for $y$ and $x$, which can lead to incorrect slope calculations.

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