If a line contains the point (0, -1) and has a slope of 2, then which of the following points also lies on the line?
(0, 1)
(1, 1)
(2, 1)
the change in y has to be twice the change in x.
Looks like (1,1), since (1,1) = (0+1, -1+2)
To determine which of the given points lies on the line, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.
Given that the line contains the point (0, -1) and has a slope of 2, we can substitute these values into the point-slope form:
y - (-1) = 2(x - 0)
Simplifying the equation, we get:
y + 1 = 2x
Now, let's test which of the given points satisfy this equation:
For the point (0, 1):
y + 1 = 2(0)
y + 1 = 0
This equation is not satisfied, so (0, 1) does not lie on the line.
For the point (1, 1):
y + 1 = 2(1)
y + 1 = 2
y = 1
This equation is satisfied, so (1, 1) lies on the line.
For the point (2, 1):
y + 1 = 2(2)
y + 1 = 4
y = 3
This equation is not satisfied, so (2, 1) does not lie on the line.
Therefore, the point (1, 1) is the only point among the given options that lies on the line.