Real World Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

How do you calculate the rate of change from a graph?

Back

The rate of change can be calculated by finding the change in y (vertical change) divided by the change in x (horizontal change), often referred to as 'rise over run'.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, showing an inverse relationship between the two variables.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What is a real-world example of a linear equation?

Back

A real-world example of a linear equation is a budget where you start with a certain amount of money and spend a fixed amount each week.

Front

How can you represent a linear equation in a table?

Back

A linear equation can be represented in a table by listing pairs of x and y values that satisfy the equation.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line, meaning it has a constant rate of change.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) represents the y-intercept of the linear equation, indicating where the line crosses the y-axis.