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.

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 steep the line is.

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 the value of y when x is 0.

Front

How do you write an equation from a word problem involving a flat fee and a variable cost?

Back

Identify the fixed cost and the variable cost, then write the equation as C = fixed cost + (variable cost per unit * number of units).

Front

If a service costs $50 plus $8 per mile, what is the equation for total cost (C) for m miles?

Back

C = 8m + 50

Front

How do you represent a situation where a cost increases with time in a linear equation?

Back

Identify the initial cost and the cost per time unit, then write the equation as C = initial cost + (cost per time unit * time).

Front

What is the equation for renting a paddle boat that costs $15 plus $2 per hour?

Back

C = 2h + 15

Front

How do you translate a verbal statement into a linear equation?

Back

Identify the variables and constants in the statement, then express the relationship using an equation.

Front

What does the equation 2x + 5 = 15 represent?

Back

It represents a situation where two times a number (x) plus five equals fifteen.

Front

How can you determine the equation of a line from a graph?

Back

Identify two points on the line, calculate the slope (rise over run), and use the slope-intercept form to write the equation.