Writing Linear Equations from 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.

Front

What does 'slope' mean in a linear equation?

Back

The slope is a number that describes the steepness and direction of a line. It is calculated as the change in y divided by the change in x (rise/run).

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 do you write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and translate the relationship into an equation.

Front

In the equation S = 4t + 0.95d, what do S, t, and d represent?

Back

S represents Norb's total salary, t represents the number of hours worked, and d represents the dollars earned in tips.

Front

What does the equation s = 3 + 2p represent in Lisa's shopping scenario?

Back

This equation shows that the number of shirts (s) Lisa bought is 3 more than twice the number of pants (p) she purchased.

Front

In the equation c = 0.12m + 8, what does c represent?

Back

c represents the total cost of phone service for one month, where m is the number of minutes used.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term represents a fixed value that does not change with the variable. It often represents a starting point or initial condition.

Front

How can you determine the height of the Nurek Dam using the equation 2x + 35 = 635?

Back

You can solve for x, which represents the height of the Nurek Dam, by isolating x in the equation.

Front

What does the equation C = 2h + 15 represent in the context of renting a paddle boat?

Back

This equation indicates that the total cost (C) to rent the boat is $15 plus $2 for each hour (h) of use.