Write Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that models 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

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

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

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting point of the linear relationship on the y-axis.

Front

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

Back

Identify the variables, determine the fixed costs and variable costs, and then express the relationship in the form y = mx + b.

Front

What is the equation for a situation where a fixed cost is added to a variable cost?

Back

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

Front

In the equation y = 20x + 100, what do the numbers 20 and 100 represent?

Back

In this equation, 20 represents the amount saved per week (variable cost), and 100 represents the initial amount in the savings account (fixed cost).

Front

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

Back

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

Front

What is the significance of the delivery fee in the equation y = 30 + 12.50x?

Back

The delivery fee of $30 is a fixed cost that is added to the total cost of the meal, which varies based on the number of people (x).

Front

How do you interpret the negative slope in the equation y = -3x + 20?

Back

A negative slope indicates that as x increases (months), the value of y (money left on the gift card) decreases.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.