Questions: Find the slope of the line that passes through the following points. Simplify your answer. (1,4) and (-9,-10)

Find the slope of the line that passes through the following points. Simplify your answer. (1,4) and (-9,-10)
Transcript text: Find the slope of the line that passes through the following points. Simplify your answer. \[ (1,4) \text { and }(-9,-10) \]
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Solution

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Solution Steps

To find the slope of the line that passes through two points, we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \((x_1, y_1)\) and \((x_2, y_2)\) are the given points.

Solution Approach
  1. Identify the coordinates of the two points.
  2. Substitute the coordinates into the slope formula.
  3. Simplify the fraction to get the slope.
Step 1: Identify the Points

The given points are \((x_1, y_1) = (1, 4)\) and \((x_2, y_2) = (-9, -10)\).

Step 2: Apply the Slope Formula

Using the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] we substitute the values: \[ m = \frac{-10 - 4}{-9 - 1} \]

Step 3: Simplify the Expression

Calculating the numerator and denominator: \[ m = \frac{-14}{-10} = \frac{14}{10} \] This simplifies to: \[ m = \frac{7}{5} \]

Final Answer

The slope of the line that passes through the points \((1, 4)\) and \((-9, -10)\) is \(\boxed{\frac{7}{5}}\).

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