Linear Equations from Tables and Graphs

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 (m) represent in a linear equation?

Back

The slope (m) 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 one-unit increase in x.

Front

What is the y-intercept (b) in a linear equation?

Back

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

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the rate of change (slope), and the starting value (y-intercept), then write the equation in the form y = mx + b.

Front

If a linear equation is y = 2x + 5, what is the slope?

Back

The slope is 2.

Front

If a linear equation is y = -3x + 4, what is the y-intercept?

Back

The y-intercept is 4.

Front

What does it mean if the slope of a line is positive?

Back

A positive slope means that as x increases, y also increases, indicating a direct relationship between the two variables.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope means that as x increases, y decreases, indicating an inverse relationship between the two variables.

Front

How can you find the rate of change from a table of values?

Back

Calculate the change in y divided by the change in x (Δy/Δx) between two points.

Front

What is the rate of change in the equation y = 5x + 10?

Back

The rate of change is 5.