Slope Intercept Word Problems

Front

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

Back

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

Front

Define slope in the context of a linear equation.

Back

Slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise over run).

Front

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

Back

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

Front

Write the equation for a situation where a person has a starting amount of money and spends a fixed amount each time they make a purchase.

Back

y = starting amount - (spending amount * x), where x is the number of purchases.

Front

Write the equation for a situation where a person starts with a certain amount of money and earns a fixed amount for each hour worked.

Back

y = starting amount + (earning amount * x), where x is the number of hours worked.

Front

How do you determine the slope from a word problem involving money spent over time?

Back

Identify the amount spent per time unit; this value represents the slope (m) in the equation.

Front

In the equation y = -20x + 100, what do the coefficients represent?

Back

-20 is the slope (amount spent per day), and 100 is the y-intercept (initial amount of money).

Front

What is the significance of the negative sign in a slope-intercept equation?

Back

A negative slope indicates a decrease in the value of y as x increases, often representing spending or loss.

Front

Write the equation for a situation where a person has already completed a task and continues to complete more at a constant rate.

Back

y = rate * x + initial amount, where x is the number of additional tasks completed.

Front

How can you identify the initial value in a word problem?

Back

The initial value is typically the starting amount before any changes occur, often mentioned explicitly in the problem.