Writing Linear Equations from Word Problems

Front

What is the general form of a linear equation?

Back

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

Front

What does 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What does 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the value of y when x is 0.

Front

How do you write a linear equation from a word problem involving a fixed cost and a variable cost?

Back

Identify the fixed cost as the y-intercept (b) and the variable cost per unit as the slope (m). Then, use the form y = mx + b.

Front

What is the slope in the equation y = 2x + 15?

Back

The slope in the equation y = 2x + 15 is 2.

Front

How can you determine the y-intercept from the equation y = 25x + 40?

Back

The y-intercept can be determined from the equation y = 25x + 40, which is 40 (the value of y when x = 0).

Front

Write a linear equation for a situation where a person saves $50 per month starting with $200.

Back

The equation is y = 50x + 200, where y is the total savings after x months.

Front

In the context of a word problem, what does it mean if the slope is negative?

Back

A negative slope indicates that as x increases, y decreases, representing a decrease in the quantity being measured.

Front

How would you write an equation for a situation where a car rental costs $30 per day plus a one-time fee of $50?

Back

The equation is y = 30x + 50, where y is the total cost and x is the number of days rented.

Front

What is the significance of the y-intercept in a real-world scenario?

Back

The y-intercept represents the starting value or initial condition before any changes occur.