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 relationship?

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 much y changes for a one-unit increase in 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 a linear relationship where the cost (C) is $25 for a house call plus $40 per hour?

Back

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

Front

If a pizza costs $2 per topping and has a base cost of $4, what is the equation for the total cost (y) based on the number of toppings (x)?

Back

y = 2x + 4.

Front

What does it mean if a linear equation has a negative slope?

Back

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

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 is the significance of the equation y = 120 - 25x in a real-world context?

Back

This equation represents a situation where a quantity (y) decreases by 25 units for every increase of 1 unit in x, starting from an initial value of 120.

Front

What is the relationship between the number of decorations (d) and the total cost (C) if each decoration costs $0.75?

Back

C = 10 + 0.75d, where $10 is the base cost of the mum.