Which equations represent a linear function?
Equation 1 y=5x-2
Equation 2 y=-1/3x
Equation 3 y=x^2-3
Equation 4 y=1
linear functions graph as a straight line,
the only one which is not a straight line is
y = x^2 - 3
the x^2 term was a give-away
To determine which equations represent a linear function, you need to remember that a linear function has a constant rate of change. This means that the dependent variable (usually represented by "y") changes at a constant rate for every change in the independent variable (usually represented by "x").
Let's analyze each equation to see if it meets this criteria:
Equation 1: y = 5x - 2
The equation is in the form y = mx + b, where "m" is the slope and "b" is the y-intercept. Since this equation has a constant slope of 5, it represents a linear function.
Equation 2: y = -1/3x
Similarly, this equation is in the form y = mx, where "m" is the slope. The slope here is -1/3, which means the rate of change is constant. Therefore, it represents a linear function.
Equation 3: y = x^2 - 3
This equation is not in the form y = mx + b. It is a quadratic equation since it contains a squared term (x^2) and does not have a constant slope. Therefore, it does not represent a linear function.
Equation 4: y = 1
This equation is in the form y = b, where "b" is a constant. Since there is no "x" term, there is no change in y based on changes in x. Therefore, it represents a horizontal line, and it does represent a linear function.
So, the equations that represent a linear function are Equation 1 (y = 5x - 2), Equation 2 (y = -1/3x), and Equation 4 (y = 1). Equation 3 (y = x^2 - 3) does not represent a linear function.