Questions: Section 1.4: Problem 1 (6 points) Find the slope of the line containing the pair of points. (5,4) and (11,7) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Simplify your answer. Give an integer or a fraction.) B. The slope is undefined.

Section 1.4: Problem 1 (6 points) Find the slope of the line containing the pair of points. (5,4) and (11,7) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Simplify your answer. Give an integer or a fraction.) B. The slope is undefined.
Transcript text: Section 1.4: Problem 1 (6 points) Find the slope of the line containing the pair of points. \[ (5,4) \text { and }(11,7) \] Select the correct choice below and, if neccessary, fill in the answer box to complete your choice. A. The slope is $\square$ (Simplify your answer. Give an integer or a fraction.) B. The slope is undefined. Submit Answers Show Me Another 'ou have attempted this problem 0 times. You have 3 attempts left before new version will be requested.
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Solution

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Solution Steps

To find the slope of the line containing two points, use the formula for the slope \( m \) which is given by the difference in the y-coordinates divided by the difference in the x-coordinates: \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substitute the given points into this formula to calculate the slope.

Step 1: Identify the Given Points

The problem provides two points: \((5, 4)\) and \((11, 7)\).

Step 2: Apply the Slope Formula

The formula for the slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Step 3: Substitute the Values

Substitute the given points into the slope formula: \[ m = \frac{7 - 4}{11 - 5} = \frac{3}{6} = \frac{1}{2} \]

Final Answer

The slope of the line is \(\boxed{\frac{1}{2}}\). Therefore, the answer is A.

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