Question

Identify the independent and dependent variables in the equation y = 3x + 5

Group of answer choices

y is independent and x is dependent

x is independent and y is dependent

both x and y are independent

both x and y are dependent

Answer 1

In the equation y = 3x + 5, x is the independent variable and y is the dependent variable. The y-intercept is 5, and the slope is 3.

Step-by-step explanation:

In the linear equation y = 3x + 5, the independent variable is x, and the dependent variable is y. This is because in a function, the value of the independent variable is chosen freely, and the value of the dependent variable is determined by the chosen value of the independent one. Generally in algebra, when we plot this function on a graph with two axes, the x-axis is the horizontal axis representing the independent variable, and the y-axis is the vertical axis representing the dependent variable.

The y-intercept of this equation is 5, which is the point where the graph of the equation crosses the y-axis. This happens when the independent variable x is equal to 0. The coefficient of the independent variable x, which is 3 in this case, is the slope of the line. The slope represents the rate at which y increases as x increases.

Answer 2

A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.