Linear Functions (A1.2.1.2.1)

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function 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 unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does the coordinate (2,3) mean in a graph of a linear function?

Back

The coordinate (2,3) means that when the independent variable (x) is 2, the dependent variable (y) is 3.

Front

If a linear function is represented as y = 5x + 2, what is the slope?

Back

The slope of the function y = 5x + 2 is 5.

Front

What is the formula to calculate the number of items produced based on a linear function?

Back

The formula is typically in the form y = mx + b, where y is the total number of items produced, m is the rate of production per unit of time, x is the time, and b is the initial quantity.

Front

How do you determine the number of pies that can be made from a given number of apples?

Back

To determine the number of pies, subtract the number of rotten apples from the total apples, then divide the remaining apples by the number of apples needed per pie.

Front

What does the equation y = 8x - 5 represent in a real-world context?

Back

In this context, y represents the total money earned from selling x pounds of tilapia, with a selling price of $8 per pound and a fixed cost of $5.

Front

How can you find out how long it takes to reach a certain distance using a linear function?

Back

To find the time to reach a certain distance, rearrange the linear function to solve for x, where y is the desired distance.