Applications of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in 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 represents the rate of change of the function; it indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you find the slope between two points?

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 a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is a point on a linear graph?

Back

A point on a linear graph is a specific coordinate (x, y) that represents a solution to the linear equation.

Front

How can you represent a real-world situation with a linear equation?

Back

You can represent a real-world situation with a linear equation by identifying the variables, determining the slope and y-intercept, and forming the equation based on the context.

Front

What is the equation of a line that passes through the point (0, 4) with a slope of 3?

Back

The equation is y = 3x + 4.

Front

If a fitness club starts with 80 members and gains 15 members each month, what is the linear equation representing this situation?

Back

The equation is y = 15x + 80, where x is the number of months.