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Algebra Difficulty: Medium

A line passes through the points $left parenthesis 4 comma 6 right parenthesis$ and $left parenthesis 15 comma 24 right parenthesis$ in the xy-plane. What is the slope of the line?

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Explanation

The correct answer is $StartFraction 18 Over 11 EndFraction$ . For a line that passes through the points $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ in the xy-plane, the slope of the line can be calculated using the slope formula, $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . It's given that a line passes through the points $left parenthesis 4 comma 6 right parenthesis$ and $left parenthesis 15 comma 24 right parenthesis$ in the xy-plane. Substituting $left parenthesis 4 comma 6 right parenthesis$ for $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis 15 comma 24 right parenthesis$ for $left parenthesis x 2 comma y 2 right parenthesis$ in the slope formula, $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , yields $m = \frac{24 - 6}{15 - 4}$ , or $m = \frac{18}{11}$ . Therefore, the slope of the line is $StartFraction 18 Over 11 EndFraction$ . Note that 18/11 and 1.636 are examples of ways to enter a correct answer.