Writing Linear Equations

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 the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

The y-intercept (b) represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = -2x + 4?

Back

The slope of the line is -2.

Front

How can 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 and the variable cost per unit as the slope, then write the equation in the form y = mx + b.

Front

In the equation y = 40 - 2x, what does the -2 represent?

Back

The -2 represents the rate at which the lunch account decreases each day.

Front

What is the significance of the delivery fee in the equation y = 30 + 12.5x?

Back

The delivery fee of $30 is the fixed cost (y-intercept) that is added to the total cost.

Front

How do you convert a table of values into a linear equation?

Back

Identify the slope using two points from the table and then use one of the points to find the y-intercept.

Front

What is the relationship between the slope and the direction of a line?

Back

A positive slope indicates the line rises from left to right, while a negative slope indicates it falls from left to right.