Question 3.3.5: Find the slope of the line through (-2, 1) and (5, -4)....
Find the slope of the line through (-2, 1) and (5, -4).
To find the slope of a line given two points, we can use the formula:
Slope = (change in y-coordinates) / (change in x-coordinates)
Step 1:
Identify the coordinates of the two points given. Let's call them (x1, y1) and (x2, y2).
Step 2:
Calculate the change in y-coordinates by subtracting y1 from y2.
Step 3:
Calculate the change in x-coordinates by subtracting x1 from x2.
Step 4:
Divide the change in y-coordinates by the change in x-coordinates to find the slope.
In this case, we have the points (-2, 1) and (5, -4).
Step 5:
The coordinates of the first point are (x1, y1) = (-2, 1) and the coordinates of the second point are (x2, y2) = (5, -4).
Step 6:
The change in y-coordinates is -4 - 1 = -5.
Step 7:
The change in x-coordinates is 5 - (-2) = 7.
Step 8:
The slope is (-5) / 7.
Therefore, the slope of the line passing through these two points is -5/7.
Final Answer
It makes no difference which ordered pair we call \left(x_1, y_1\right) and which we call \left(x_2, y_2\right).
\text { Slope }=m=\frac{y_2~-~y_1}{x_2~-~x_1}=\frac{-4~-~1}{5~-~(-2)}=\frac{-5}{7}
The slope is -\frac{5}{7}. Every vertical change of – 5 units (down 5 units) is accompanied by a horizontal change of 7 units (to the right 7 units). (See Figure 8.)
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