7th Grade Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of 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 in a linear equation?

Back

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

Front

What is the y-intercept in a linear equation?

Back

The y-intercept 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 an equation for a linear relationship?

Back

To write an equation for a linear relationship, identify the slope (m) and the y-intercept (b) from a graph or a table of values, and use the formula y = mx + b.

Front

What is the equation for the total cost (C) if an electrician charges $25 for a house call and $40 per hour?

Back

C = 25 + 40h, where h is the number of hours worked.

Front

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

Back

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

Front

What does the equation y = 120 - 25x represent in a real-world context?

Back

It represents a situation where there are 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

What is a function in mathematics?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficients indicate the slope and the y-intercept. The coefficient of x (slope) shows the rate of change, while the constant term (y-intercept) shows the starting value.

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the one that is changed or controlled in an experiment (usually x), while the dependent variable is the one that is measured or affected (usually y).