Slope intercept from word problems

Front

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

Back

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

Front

How do you identify the slope in a word problem involving a linear equation?

Back

The slope represents the rate of change in the context of the problem, often described as 'per unit' (e.g., dollars per hour, feet per minute).

Front

What does the y-intercept represent in a real-world scenario?

Back

The y-intercept represents the starting value or initial condition before any changes occur, such as fixed costs or initial amounts.

Front

In the equation y = 30x + 20, what do the numbers 30 and 20 represent?

Back

In this equation, 30 is the slope (cost per hour), and 20 is the y-intercept (initial transportation fee).

Front

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

Back

Identify the fixed costs (y-intercept) and the variable costs (slope), then express the relationship in the form y = mx + b.

Front

What is the significance of a negative slope in a word problem?

Back

A negative slope indicates a decrease in value over time or with each unit, such as spending money or losing height.

Front

How do you interpret the equation y = -3x + 20 in a real-world context?

Back

This equation indicates that Sandra starts with $20 and spends $3 each month, decreasing her balance over time.

Front

What does the variable 'x' typically represent in application-based linear equations?

Back

The variable 'x' usually represents the independent variable, often time or quantity, depending on the context of the problem.

Front

How can you determine the total cost from a rental service using a linear equation?

Back

By identifying the hourly rate (slope) and any fixed fees (y-intercept), you can write the equation to calculate total cost.

Front

What is the first step in solving a word problem that requires a linear equation?

Back

Read the problem carefully to identify the quantities involved and their relationships, including fixed and variable costs.