Question

if the slopes of two lines are different and their product is not equal to -1, then the two lines are neither parallel nor perpendicular.

example 2
determine whether the two lines are parallel or perpendicular.

table
x | y
1 | 3
2 | 6
3 | 9
4 | 12

graph showing a line passing through points such as (0, -1) and (1, 1)

solution
in order to compare the two lines, find the slope of both the lines.

value: 1
find the slope of the line given in the table.
a. 3
b. -3
c. -1/3
d. 1/3

Explanation:

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<reasoning>

Identify points from the table

Using the points \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (2, 6)\).

Calculate the slope

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 3}{2 - 1} = 3
\]
</reasoning>

<answer>
<mcq-correct>(a) 3</mcq-correct>
<mcq-option>(b) -3</mcq-option>
<mcq-option>(c) -1/3</mcq-option>
<mcq-option>(d) 1/3</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify points from the table

Using the points \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (2, 6)\).

Calculate the slope

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 3}{2 - 1} = 3
\]
</reasoning>

<answer>
<mcq-correct>(a) 3</mcq-correct>
<mcq-option>(b) -3</mcq-option>
<mcq-option>(c) -1/3</mcq-option>
<mcq-option>(d) 1/3</mcq-option>
</answer>

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