Question
Find the slopes of the lines \( l_{1} \) and \( l_{2} \) defined by the two given points. Then determine whether \( l_{1} \) and \( l_{2} \) are par perpendicular, or neither. \( 1:(13,-5) \) and \( (10,-6) \) Part: \( 0 / 3 \) Part 1 of 3 The slope of \( l_{1} \) is is
Ask by Clark Reid. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope of \( l_{1} \) is \( \frac{1}{3} \).
Solution
To find the slope of the line \( l_{1} \) defined by the points \( (13, -5) \) and \( (10, -6) \), we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) = (13, -5) \) and \( (x_2, y_2) = (10, -6) \).
Now, let's substitute the values into the formula:
1. Calculate \( y_2 - y_1 \):
\[
y_2 - y_1 = -6 - (-5) = -6 + 5 = -1
\]
2. Calculate \( x_2 - x_1 \):
\[
x_2 - x_1 = 10 - 13 = -3
\]
3. Now, substitute these results into the slope formula:
\[
m_{1} = \frac{-1}{-3} = \frac{1}{3}
\]
Thus, the slope of \( l_{1} \) is \( \frac{1}{3} \).
Now, let's proceed to find the slope of the second line \( l_{2} \) defined by the points. Please provide the coordinates for the second line \( l_{2} \) so we can continue.
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Simplify this solution Beyond the Answer
To find the slope of line \( l_{1} \) defined by the points \( (13, -5) \) and \( (10, -6) \), we can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Assigning the points \( (x_1, y_1) = (13, -5) \) and \( (x_2, y_2) = (10, -6) \): \[ m_{l_{1}} = \frac{-6 - (-5)}{10 - 13} = \frac{-6 + 5}{10 - 13} = \frac{-1}{-3} = \frac{1}{3} \] The slope of \( l_{1} \) is \( \frac{1}{3} \). Now let's find the slopes for line \( l_{2} \) defined by the two points, say \( (x_3, y_3) \) and \( (x_4, y_4) \). If you provide those points, I can assist further in determining if the lines are perpendicular, parallel, or neither!
