High School

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Find the slopes of the lines [tex] l_1 [/tex] and [tex] l_2 [/tex] defined by the two given points. Then determine whether [tex] l_1 [/tex] and [tex] l_2 [/tex] are parallel, perpendicular, or neither.

Points for [tex] l_1 [/tex]: [tex](3, -5)[/tex] and [tex](7, -1)[/tex]

Points for [tex] l_2 [/tex]: [tex](1, -5)[/tex] and [tex](4, -2)[/tex]

Part 1 of 3

The slope of [tex] l_1 [/tex] is [tex]\square[/tex]

Answer :

To find the slope of the line [tex]\( l_1 \)[/tex] that goes through the points [tex]\((3, -5)\)[/tex] and [tex]\((7, -1)\)[/tex], we use the formula for the slope of a line given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:

[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]

For line [tex]\( l_1 \)[/tex]:

- [tex]\((x_1, y_1) = (3, -5)\)[/tex]
- [tex]\((x_2, y_2) = (7, -1)\)[/tex]

Substitute these values into the slope formula:

[tex]\[
m = \frac{-1 - (-5)}{7 - 3}
\][/tex]

Simplify the expression:

- The numerator becomes: [tex]\(-1 + 5 = 4\)[/tex]
- The denominator becomes: [tex]\(7 - 3 = 4\)[/tex]

So, the slope [tex]\( m \)[/tex] is:

[tex]\[
m = \frac{4}{4} = 1
\][/tex]

Therefore, the slope of [tex]\( l_1 \)[/tex] is [tex]\( 1 \)[/tex].

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