6.3 Applications of Linear Equations

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

How do you calculate the normal price after a percentage discount?

Back

To find the normal price after a discount, use the formula: Normal Price = Sale Price / (1 - Discount Rate). For example, if the sale price is $195.60 and the discount is 20%, the normal price is $195.60 / (1 - 0.20) = $244.50.

Front

What is the equation for total cost when there is a fixed fee and a variable cost?

Back

The total cost (c) can be expressed as c = fixed fee + (variable cost per unit * number of units). For example, if the fixed fee is $4 and the variable cost is $2.75 per bucket, the equation is c = 2.75b + 4.

Front

How do you solve for a variable in a linear equation?

Back

To solve for a variable, isolate the variable on one side of the equation using inverse operations. For example, in the equation c = 2.75b + 4, to find b when c = 31.50, rearrange to 31.50 - 4 = 2.75b, then solve for b.

Front

What is commission and how is it calculated?

Back

Commission is a fee paid to an employee based on the sales they make. It is calculated as a percentage of the sale price. For example, if the commission rate is 7% on a $345 sale, the commission is 0.07 * 345 = $24.15.

Front

How do you calculate the final price including sales tax?

Back

To calculate the final price including sales tax, use the formula: Final Price = Price + (Price * Sales Tax Rate). For example, for a $990 TV with a 9% sales tax, the final price is 990 + (990 * 0.09) = $1,079.10.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two quantities to be directly proportional?

Back

Two quantities are directly proportional if they increase or decrease at the same rate. This can be expressed as y = kx, where k is a constant.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x = 0.

Front

How can you represent a real-world situation with a linear equation?

Back

A real-world situation can be represented with a linear equation by identifying the fixed and variable costs, and expressing the total cost as a function of the number of units.