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Chapter 1: Problem 138

Determine whether the statement is true or false. Justify your answer. The line through (-8,2) and (-1,4) and the line through (0,-4) and (-7,7) are parallel.

Short Answer

Expert verified
The statement is false. The slopes of the given lines are not equal, so the lines are not parallel.

Step by step solution

01

Determine the slope for the first line

The slope of a line that goes through the points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula \[slope = \frac{y_2 - y_1}{x_2 - x_1}\]. Using the points (-8,2) and (-1,4), the slope of the first line is given by \[\frac{4 - 2}{-1 - (-8)} = \frac{2}{7}\]
02

Determine the slope for the second line

Following the same process and using the points (0,-4) and (-7,7), the slope of the second line is given by \[\frac{7 - (-4)}{-7 - 0} = \frac{11}{-7} = -\frac{11}{7}\]
03

Compare the slopes

The slope of the first line is \(\frac{2}{7}\), and the slope of the second line is \(-\frac{11}{7}\). Because these values are not equal, the lines are not parallel.

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