Tables, Graphs, 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

How do you determine if a relationship is proportional?

Back

A relationship is proportional if it can be represented by a linear equation that passes through the origin (0,0). In a proportional relationship, the ratio of the two quantities remains constant.

Front

What does the slope of a line represent in a graph?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much the dependent variable changes for a unit change in the independent variable.

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 represented by the value of b in the equation y = mx + b.

Front

How can you write an equation from a table of values?

Back

To write an equation from a table of values, identify the relationship between the variables, determine the slope (rate of change), and find the y-intercept, then use the slope-intercept form of a linear equation.

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships have a constant ratio and pass through the origin, while non-proportional relationships do not have a constant ratio and do not pass through the origin.

Front

How do you interpret the equation w = 50m in a real-world context?

Back

In this equation, w represents the total words typed, and m represents the minutes spent typing. It indicates that for every minute, 50 words are typed.

Front

What does the equation y = x + 5 represent?

Back

This equation represents a linear relationship where for every unit increase in x, y increases by 1, and the line crosses the y-axis at 5.

Front

How can you identify the slope from an equation?

Back

In the slope-intercept form of a linear equation (y = mx + b), the slope is represented by the coefficient m.

Front

What is the significance of the equation 40x + 150 in a savings context?

Back

This equation represents Bob's total savings after x months, where 150 is the initial amount and 40 is the amount saved each month.