Question
Find the slope \( m \) of the line through the following pair of points and draw the line through the points. \( (-5,1),(-4,-4) \) Answer exactly. \( m=\square \)
Ask by Robbins Huff. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( m = -5 \)
Solution
1. To find the slope \( m \) of the line through the points \((-5, 1)\) and \((-4, -4)\), we use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
2. Substitute the given points \((x_1, y_1) = (-5, 1)\) and \((x_2, y_2) = (-4, -4)\):
\[
m = \frac{-4 - 1}{-4 - (-5)} = \frac{-5}{1} = -5
\]
3. The slope of the line is:
\[
m = -5
\]
4. The equation of the line can be written using the point-slope form:
\[
y - 1 = -5(x + 5)
\]
Thus, the final answer is:
\[
m = -5
\]
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Simplify this solution Bonus Knowledge
To find the slope \( m \) of the line through the points \( (-5,1) \) and \( (-4,-4) \), you can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (-5, 1) \) and \( (x_2, y_2) = (-4, -4) \). Plugging in these values: \[ m = \frac{-4 - 1}{-4 - (-5)} = \frac{-5}{-4 + 5} = \frac{-5}{1} = -5 \] So the slope \( m \) is \( -5 \). Now for drawing the line through those points: You can plot the points \( (-5, 1) \) and \( (-4, -4) \) on a coordinate plane. Connect these points with a straight line, and extend the line across the graph for visualization. The negative slope indicates that as you move from left to right, the line will decrease steeply.
