Which of the following points is on the line y = 2x + 1?
(0, 0)
(1, 3)
(2, 4)
(5, 2)
To determine if a point is on the line y = 2x + 1, we substitute the x and y values of the point into the equation and check if it is a true statement.
Let's check each option:
(0, 0):
y = 2x + 1
0 = 2(0) + 1
0 = 0 + 1
0 = 1
This is false, so (0, 0) is not on the line.
(1, 3):
y = 2x + 1
3 = 2(1) + 1
3 = 2 + 1
3 = 3
This is true, so (1, 3) is on the line.
(2, 4):
y = 2x + 1
4 = 2(2) + 1
4 = 4 + 1
4 = 5
This is false, so (2, 4) is not on the line.
(5, 2):
y = 2x + 1
2 = 2(5) + 1
2 = 10 + 1
2 = 11
This is false, so (5, 2) is not on the line.
Therefore, the point (1, 3) is the only one that is on the line y = 2x + 1.
Which of the following is not a linear equation?
y = 4x − 9
y = 3
y = x2 + 1
5 = x + y
The equation that is not a linear equation is y = x^2 + 1.
This equation is a quadratic equation because it includes a squared term (x^2), which makes it a non-linear equation.
The other three equations are linear equations because they have a maximum degree of 1 and do not include any squared or higher terms.
or which of the following equations should values other than −1, 0, and 1 be chosen for the inputs?
y = 13x + 5
y = −3x − 5
y = 3x + 15
y = 3x
The equation for which values other than -1, 0, and 1 should be chosen for the inputs is y = 3x.
This is because in equations y = 13x + 5, y = -3x - 5, and y = 3x + 15, any value can be chosen for x, including values other than -1, 0, and 1.
However, in the equation y = 3x, if x is chosen to be -1, 0, or 1, the resulting value of y will also be -3, 0, or 3 respectively. For any other value of x, the resulting value of y will be different. Thus, in order to choose values other than -1, 0, and 1 for the inputs, the equation y = 3x should be selected.
To determine which point is on the line y = 2x + 1, substitute the x and y coordinates of each point into the equation and check if the equation holds true.
For the first point (0, 0):
y = 2x + 1
0 = 2(0) + 1
0 = 0 + 1
0 = 1
Since 0 does not equal 1, the point (0, 0) is not on the line.
For the second point (1, 3):
y = 2x + 1
3 = 2(1) + 1
3 = 2 + 1
3 = 3
Since 3 equals 3, the point (1, 3) is on the line.
For the third point (2, 4):
y = 2x + 1
4 = 2(2) + 1
4 = 4 + 1
4 = 5
Since 4 does not equal 5, the point (2, 4) is not on the line.
For the fourth point (5, 2):
y = 2x + 1
2 = 2(5) + 1
2 = 10 + 1
2 = 11
Since 2 does not equal 11, the point (5, 2) is not on the line.
In conclusion, the point (1, 3) is the only point that lies on the line y = 2x + 1.
To determine which of the given points is on the line y = 2x + 1, we need to substitute the x and y values of each point into the equation and see if both sides of the equation are equal.
Let's check each point:
(0, 0):
Substituting x = 0 and y = 0 into the equation, we get:
0 = 2(0) + 1
0 = 0 + 1
0 = 1
Since the left side of the equation (0) does not equal the right side of the equation (1), the point (0, 0) is not on the line y = 2x + 1.
(1, 3):
Substituting x = 1 and y = 3 into the equation, we get:
3 = 2(1) + 1
3 = 2 + 1
3 = 3
Since both sides of the equation are equal, the point (1, 3) is on the line y = 2x + 1.
(2, 4):
Substituting x = 2 and y = 4 into the equation, we get:
4 = 2(2) + 1
4 = 4 + 1
4 = 5
Since the left side of the equation (4) does not equal the right side of the equation (5), the point (2, 4) is not on the line y = 2x + 1.
(5, 2):
Substituting x = 5 and y = 2 into the equation, we get:
2 = 2(5) + 1
2 = 10 + 1
2 = 11
Since the left side of the equation (2) does not equal the right side of the equation (11), the point (5, 2) is not on the line y = 2x + 1.
Therefore, the only point on the line y = 2x + 1 is (1, 3).