Questions: Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. (-2,-3) and (3,6) (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the parallel line is (Type an integer or a simplified fraction.) B. The slope of the parallel line is undefined.

Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. (-2,-3) and (3,6) (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the parallel line is (Type an integer or a simplified fraction.) B. The slope of the parallel line is undefined.
Transcript text: Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. $(-2,-3)$ and $(3,6)$ (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the parallel line is $\square$ (Type an integer or a simplified fraction.) B. The slope of the parallel line is undefined.
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Solution

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Solution Steps

Step 1: Identify the slope of the given line

The given line is defined through two points \((x_1, y_1) = (-2, -3)\) and \((x_2, y_2) = (3, 6)\). Using the formula \(m = (y_2 - y_1) / (x_2 - x_1)\), we find the slope of the given line to be \(m = 1.8\).

Step 2: Determine the slope of the line that is parallel or perpendicular

The slope of a line parallel to the given line is the same as the slope of the given line, \(m = 1.8\).

Final Answer: The slope of the line that is parallel to the given line is 1.8.

Step 1: Identify the slope of the given line

The given line is defined through two points \((x_1, y_1) = (-2, -3)\) and \((x_2, y_2) = (3, 6)\). Using the formula \(m = (y_2 - y_1) / (x_2 - x_1)\), we find the slope of the given line to be \(m = -0.56\).

Step 2: Determine the slope of the line that is parallel or perpendicular

The slope of a line perpendicular to the given line is the negative reciprocal of the slope of the given line, \(m' = -1/m = -0.56\).

Final Answer: The slope of the line that is perpendicular to the given line is -0.56.
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