Question

A line contains the points (-4,1) and (4,6). Decide weather or not each of these points are also on the line.

a.(0,3.5)
b.(12,11)
c.(80,50)
d.(-1,2.875)

Answer 1

Using the point-slope form of the linear equation that passes through (-4,1) and (4,6), we found that the points (12,11) and (-1,2.875) are on the line, whereas (0,3.5) and (80,50) are not on the line.

Step-by-step explanation:

To determine whether the given points lie on the line that contains the points (-4,1) and (4,6), we need to find the slope of the line and see if all the points satisfy the linear equation formed by these two points. We can calculate the slope using the formula slope (m) = (y2 - y1) / (x2 - x1). Using the given points (-4,1) and (4,6), we get the slope as:

m = (6 - 1) / (4 - (-4)) = 5 / 8

Now, we can use the point-slope form of the line to create the equation y - y1 = m(x - x1). Using one of the given points, say (-4,1), we have:

y - 1 = (5/8)(x + 4)

This equation represents the line. We can now test each of the provided points.

1. Point (0,3.5): If we plug x = 0 into the equation, we get y = 1 + (5/8)(0 + 4) = 4.5, which is not equal to 3.5. So this point is not on the line.
2. Point (12,11): If we plug x = 12 into the equation, we get y = 1 + (5/8)(12 + 4) = 11, which is equal to the y-value of the point. So this point is on the line.
3. Point (80,50): If we plug x = 80 into the equation, we get y = 1 + (5/8)(80 + 4) = 53.5, which is not equal to 50. So this point is not on the line.
4. Point (-1,2.875): If we plug x = -1 into the equation, we get y = 1 + (5/8)(-1 + 4) = 2.875, which is equal to the y-value of the point. So this point is on the line.

In conclusion, points (12,11) and (-1,2.875) lie on the line, while points (0,3.5) and (80,50) do not.