Writing Linear Equations - Word Problems

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope in a linear equation represent?

Back

The slope 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.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept in a linear equation represent?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

If a person saves $20 each week starting with $100, how would you represent this situation with a linear equation?

Back

y = 20x + 100, where y is the total savings after x weeks.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

A plant grows 3 cm each month starting from a height of 5 cm. Write the linear equation for this situation.

Back

y = 3x + 5, where y is the height of the plant after x months.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Sally walks 12 miles every week. Write the equation that represents the total distance walked after x weeks.

Back

y = 12x, where y is the total distance and x is the number of weeks.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the total cost equation for renting a paddle boat with a $15 deposit and $2 per hour?

Back

C = 2h + 15, where C is the total cost and h is the number of hours rented.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you identify a linear equation from a word problem?

Back

Look for constant rates of change and relationships that can be expressed in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the equation y = -25x + 120 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.

Tags

CCSS.HSF.LE.B.5