What is the slope, m, of the graph below?

Question image

Understand the Problem

The question is asking for the calculation of the slope (m) from a given graph that includes two points. This requires using the slope formula based on the coordinates of the points provided.

Answer

The slope is \( m = -2 \).
Answer for screen readers

The slope ( m ) of the graph is given by:

$$ m = -2 $$

Steps to Solve

  1. Identify the coordinates of the two points

From the graph, we have two points:

  • Point 1: $(2, -5)$
  • Point 2: $(7, -15)$
  1. Use the slope formula

The slope ( m ) between two points ((x_1, y_1)) and ((x_2, y_2)) is calculated using the formula:

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

In our case, substituting the coordinates into the formula, we have:

$$ m = \frac{-15 - (-5)}{7 - 2} $$

  1. Calculate the differences in the formula

Now calculate the differences in the formula:

  • For the numerator: $$ -15 - (-5) = -15 + 5 = -10 $$

  • For the denominator: $$ 7 - 2 = 5 $$

  1. Calculate the slope

Now, substitute the calculated values into the slope formula:

$$ m = \frac{-10}{5} $$

  1. Simplify the result

Finally, simplify:

$$ m = -2 $$

The slope ( m ) of the graph is given by:

$$ m = -2 $$

More Information

The slope reflects the steepness of the line. A slope of ( -2 ) indicates that for every 1 unit the line moves right, it moves 2 units down.

Tips

  • Forgetting to use parentheses when calculating differences in the slope formula.
  • Mixing up the coordinates; always remember that ((x_1, y_1)) should correspond to the first point and ((x_2, y_2)) to the second point.
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