Interpreting Linear Equations

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

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

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating the starting point of the line on the y-axis.

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

How can you identify the x-intercept from a linear equation?

Back

The x-intercept can be found by setting y to 0 in the equation and solving for x.

Front

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

Back

The delivery fee represents a fixed cost that is added to the total cost of the meal, regardless of the number of people.

Front

In the equation y = 7x + 20, what does the term 20 represent?

Back

The term 20 represents the initial amount of money Jerry has before he starts working.

Front

What are the x- and y-intercepts of the equation 3x + 4y = 20?

Back

The x-intercept is (20/3, 0) and the y-intercept is (0, 5).

Front

How do you interpret the slope of -4/3 in a real-world context?

Back

A slope of -4/3 indicates that for every 3 units increase in x, y decreases by 4 units, suggesting a negative relationship between the two variables.

Front

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

Back

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