The given points on the line are (-4, 3), (-2, 2), (0, 1), (1, 1/2), and (4, -1).
By examining the values of X and Y, we can see that as we move from left to right along the line, the Y-values are decreasing. This indicates that the line has a negative slope.
We can calculate the slope of the line using the formula: slope = (change in Y) / (change in X).
For the points (-4, 3) and (-2, 2):
slope = (2-3) / (-2-(-4)) = (-1) / (2) = -1/2
For the points (-2, 2) and (0, 1):
slope = (1-2) / (0-(-2)) = (-1) / (2) = -1/2
For the points (0, 1) and (1, 1/2):
slope = (1/2-1) / (1-0) = (-1/2) / (1) = -1/2
For the points (1, 1/2) and (4, -1):
slope = (-1-1/2) / (4-1) = (-3/2) / (3) = -1/2
As we can see, the slope of the line remains constant at -1/2 for all pairs of consecutive points. Therefore, the line can be described by the equation y = (-1/2)x + b, where b is the y-intercept of the line.
To find the y-intercept, we can select any point on the line and substitute its coordinates into the equation. Let's use the point (0, 1):
1 = (-1/2)(0) + b
1 = b
Therefore, the equation of the line is y = (-1/2)x + 1.
Examine the following table that represents some points on a line.
X Y
-4 3
-2 2
0 1
1 1/2
4 -1
1 answer