Question

The slope of a line is ¾.  A different line passes through the points (6, 3) & (-1, 5).  Are the lines parallel?  Why or why not?

Group of answer choices

A They are parallel because they both have a slope of ¾.

B They are not parallel because their slopes are not equal.

C They are parallel because they share a common point.

D They are not parallel because they are the exact same line.



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Answer 1

They are not parallel because their slopes are not equal.

Solution:

Given that,

$\text{ slope of line } =\frac{3}{4}$

A different line passes through the points (6, 3) & (-1, 5)

Find the slope of this line

$m = \frac{y_2-y_1}{x_2-x_1}$

From given,

$(x_1, y_1) = (6, 3)\\\\(x_2, y_2) = (-1, 5)$

Substituting we get,

$m = \frac{5-3}{-1-6}\\\\m = \frac{2}{-7}$

For two lines are parallel, then their slopes must be equal

But here,

$\frac{3}{4} \neq \frac{-2}{7}$

Therefore, They are not parallel because their slopes are not equal