A line has Zero slope is when the line is parallel to the x-axis. The slope of the first pair of coordinates will have no slope or zero slopes.
The slope of a line is given by the formula,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
where (x₂,y₂) and (x₁,y₁) are the coordinates of any point on the line of slope.
1. For the first slope, the given coordinates are
(-3,2),(-1,2),(1,2),(3,2)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{2-2}{-3-3}=\dfrac{0}{-6}=0[/tex]
Thus, the slope of the line is 0. And if we plot the points on the graph we will see that the slope of the line is 0.
2. For the second slope, the given coordinates are
(-3,3),(-1,1),(1,-1),(3,-3)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{3-(-3)}{-3-3}=\dfrac{6}{-6}=-1[/tex]
Thus, the slope of the line is -1. And if we plot the points on the graph we will see that the slope of the line is -1.
3. For the third slope, the given coordinates are
(-5,-5), (0,0), (5,5)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{-5-5}{-5-5}=\dfrac{-10}{-10}=1[/tex]
Thus, the slope of the line is 1. And if we plot the points on the graph we will see that the slope of the line is 1.
4. For the fourth slope, the given coordinates are
(-2,5), (-2,0), (-2,5)
Now, if we take the first and the last point to calculate the slope of the line, we will get,
[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)} = \dfrac{5-0}{-2-(-2)}=\dfrac{5}{0}[/tex]
Thus, the slope of the line is undefined. And if we plot the points on the graph we will see that the slope of the line is undefined or at 90° from the x-axis.
Hence, the slope of the first pair of coordinates will have no slope or zero slopes.
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