Question
\( l_{1}:(13,-5) \) and \( (10,-6) \) \( l_{2}:(6,4) \) and \( (5,1) \) Part 1 of 3 The slope of \( l_{1} \) is \( \frac{1}{3} \) Part: \( \mathbf{1} / \mathbf{3} \) Part 2 of 3 The slope of \( l_{2} \) is
Ask by Elliott Campbell. in the United States
Mar 13,2025
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Answer
The slope of \( l_{2} \) is \( 3 \).
Solution
To find the slope of line \( l_{2} \) given the points \( (6, 4) \) and \( (5, 1) \), we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.
For line \( l_{2} \):
- \( (x_1, y_1) = (6, 4) \)
- \( (x_2, y_2) = (5, 1) \)
Now, we can substitute these values into the slope formula:
\[
m = \frac{1 - 4}{5 - 6}
\]
Calculating the numerator and denominator:
\[
m = \frac{-3}{-1} = 3
\]
Thus, the slope of line \( l_{2} \) is \( 3 \).
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Simplify this solution The Deep Dive
To find the slope of line \( l_{2} \) using the coordinates \( (6, 4) \) and \( (5, 1) \), you can apply the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1, y_1) = (6, 4) \) and \( (x_2, y_2) = (5, 1) \). So, plugging in the numbers gives us: \[ m = \frac{1 - 4}{5 - 6} = \frac{-3}{-1} = 3 \] Therefore, the slope of \( l_{2} \) is \( 3 \). Now, imagine painting a fence: you want it to be straight, just like those slopes! Changing the sink of each color in your slope paints will keep your fence looking just as it should! That balance between x and y is exactly how you maintain your design integrity—smooth, straight, and stunning!
