Which of the following are linear equations? Select all that apply.(1 point)
Responses
y=−x2+4
y is equal to negative x squared plus 4
y=5−2x
y is equal to 5 minus 2 over x
x−3y=3
x minus 3 y is equal to 3
y=2x
y is equal to 2 to the x th power
y=12x+3
The linear equations are:
- y=5−2x
- x−3y=3
- y=2x
- y=12x+3
The linear equations from the given options are:
1) y = 5 - 2x
(Explanation: This equation represents a line with slope -2 and y-intercept 5.)
2) x - 3y = 3
(Explanation: This equation represents a line in slope-intercept form. By rearranging the equation, we can write it as y = (1/3)x - 1, with a slope of 1/3 and y-intercept -1.)
3) y = 2x
(Explanation: This equation represents a line with a slope of 2 and y-intercept at the origin (0,0).)
4) y = 12x + 3
(Explanation: This equation represents a line with a slope of 12 and y-intercept at (0,3).)
Therefore, the linear equations from the options are:
y = 5 - 2x
x - 3y = 3
y = 2x
y = 12x + 3
To determine whether each equation is linear, we need to understand what makes an equation linear.
A linear equation is an equation in which the highest power of the variable is 1. This means that any equation with variables raised to a power other than 1 is not linear.
Let's analyze each equation:
1. y=−x^2+4
This equation has a variable (x) raised to the power of 2, which means it is NOT linear.
2. y=5−2x
This equation only has the variable (x) raised to the power of 1 (no exponent), so it is linear.
3. x−3y=3
This equation has both variables (x and y) raised to the power of 1 (no exponent), so it is linear.
4. y=2x
This equation only has the variable (x) raised to the power of 1 (no exponent), so it is linear.
5. y=12x+3
This equation only has the variable (x) raised to the power of 1 (no exponent), so it is linear.
Therefore, the linear equations from the provided options are:
- y=5−2x
- x−3y=3
- y=2x
- y=12x+3