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Answer :
To find the slope of line [tex]\( l_1 \)[/tex] using the given points [tex]\((9, -1)\)[/tex] and [tex]\((6, -4)\)[/tex], we will use the formula for calculating the slope between two points. The slope [tex]\( m \)[/tex] of a line through points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is calculated by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's apply this formula:
- For line [tex]\( l_1 \)[/tex], the points are [tex]\((9, -1)\)[/tex] and [tex]\((6, -4)\)[/tex].
- Here, [tex]\( x_1 = 9 \)[/tex], [tex]\( y_1 = -1 \)[/tex], [tex]\( x_2 = 6 \)[/tex], and [tex]\( y_2 = -4 \)[/tex].
Let's plug these values into the slope formula:
[tex]\[
m = \frac{-4 - (-1)}{6 - 9} = \frac{-4 + 1}{6 - 9} = \frac{-3}{-3}
\][/tex]
Simplifying this expression gives:
[tex]\[
m = 1.0
\][/tex]
Thus, the slope of line [tex]\( l_1 \)[/tex] is [tex]\( 1.0 \)[/tex].
Now, you can input this value into the solution for the slope of [tex]\( l_1 \)[/tex].
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's apply this formula:
- For line [tex]\( l_1 \)[/tex], the points are [tex]\((9, -1)\)[/tex] and [tex]\((6, -4)\)[/tex].
- Here, [tex]\( x_1 = 9 \)[/tex], [tex]\( y_1 = -1 \)[/tex], [tex]\( x_2 = 6 \)[/tex], and [tex]\( y_2 = -4 \)[/tex].
Let's plug these values into the slope formula:
[tex]\[
m = \frac{-4 - (-1)}{6 - 9} = \frac{-4 + 1}{6 - 9} = \frac{-3}{-3}
\][/tex]
Simplifying this expression gives:
[tex]\[
m = 1.0
\][/tex]
Thus, the slope of line [tex]\( l_1 \)[/tex] is [tex]\( 1.0 \)[/tex].
Now, you can input this value into the solution for the slope of [tex]\( l_1 \)[/tex].
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