Linear Tables, Graphs, and 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 is found by setting x to 0 in the equation and solving for y. It is the point where the line crosses the y-axis.

Front

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

Back

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

Front

What does the term 'rate of change' mean in a linear context?

Back

Rate of change refers to how much the dependent variable changes for a unit change in the independent variable. In linear equations, it is represented by the slope.

Front

What is the equation for a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls, what is the total cost equation?

Back

c = 2.75b + 4, where c is the total cost and b is the number of buckets.

Front

What does it mean if a graph has a constant slope?

Back

A constant slope means that the rate of change is the same throughout the graph, indicating a linear relationship.

Front

How can you determine if a relationship is linear from a table of values?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the relationship is linear.

Front

What is the unit rate in a linear relationship?

Back

The unit rate is the slope of the line when the x-axis represents one unit. It shows how much y changes for each one unit change in x.