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 steep the line is.

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept of a linear equation can be found by setting x to 0 in the equation and solving for y.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept represents the initial value of the dependent variable when the independent variable is zero, often providing a starting point in real-world scenarios.

Front

How can you interpret the rate of change in a real-world situation?

Back

The rate of change indicates how much one quantity changes in relation to another quantity, often expressed as a ratio or percentage.

Front

What is an example of a real-world scenario that can be modeled by a linear equation?

Back

An example is saving money over time, where you start with a certain amount and add a fixed amount each month.

Front

How do you determine the initial value from a graph?

Back

The initial value can be determined by finding the y-intercept of the graph, which is the point where the line crosses the y-axis.