Per 4 Writing Slope-Intercept Form Equation from Situations

Front

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

Back

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

Front

How do you determine the slope from a situation involving a cost?

Back

The slope represents the rate of change in cost per unit, such as dollars per mile or dollars per topping.

Front

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

Back

The y-intercept represents the initial value or starting point when x = 0.

Front

If a car depreciates at a constant rate, how is this represented in a linear equation?

Back

It is represented with a negative slope, indicating a decrease in value over time.

Front

How can you model a situation where a fixed fee is charged plus a variable cost?

Back

Use the equation y = mx + b, where m is the variable cost per unit and b is the fixed fee.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients indicate the rate of change (slope) and the starting value (y-intercept) of the function.

Front

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

Back

Identify the fixed and variable costs, assign variables, and use the slope-intercept form to create the equation.

Front

What does a positive slope indicate in a real-world context?

Back

A positive slope indicates that as one variable increases, the other variable also increases, such as cost increasing with more toppings.

Front

What does a negative slope indicate in a real-world context?

Back

A negative slope indicates that as one variable increases, the other variable decreases, such as value decreasing over time.

Front

How can you find the total cost from a linear equation?

Back

Substitute the value of x (number of units) into the equation to find the total cost (y).