Day 58 Writing Linear Equations & Expressions from Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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

How do you identify the slope in a linear equation?

Back

The slope in a linear equation is the coefficient of the variable x. It represents the rate of change of y with respect to x.

Front

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

Back

The y-intercept is the value of y when x is 0. It represents the point where the line crosses the y-axis.

Front

How can you represent a word problem as a linear equation?

Back

To represent a word problem as a linear equation, identify the quantities involved, assign variables to them, and express the relationships using mathematical operations.

Front

What is the constant term in a linear expression?

Back

The constant term in a linear expression is the value that does not change with the variable. It represents fixed costs or initial amounts.

Front

How do you convert a word problem into an expression?

Back

To convert a word problem into an expression, identify the quantities and their relationships, then use variables and mathematical operations to express these relationships.

Front

What is the significance of the startup fee in a word problem?

Back

The startup fee is a fixed cost that must be paid before any variable costs are incurred. It is represented as a constant in the expression.

Front

How do you determine the total cost from a word problem involving fixed and variable costs?

Back

To determine the total cost, add the fixed costs (constants) to the variable costs (expressed as a product of a variable and its coefficient).

Front

What does the variable represent in a linear equation derived from a word problem?

Back

The variable in a linear equation typically represents a quantity that can change, such as time, number of items, or any other measurable factor.

Front

How can you find the number of weeks needed to reach a savings goal from a word problem?

Back

To find the number of weeks needed to reach a savings goal, set up the equation based on the initial amount, the amount saved per week, and the total savings goal, then solve for the variable representing weeks.