Applying Linear Functions Assignment

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 steep the line is.

Front

What is the y-intercept of a linear function?

Back

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

Front

How do you determine 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 it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they are parallel to each other and will never intersect.

Front

What is the significance of a greater slope in a linear function?

Back

A greater slope indicates a steeper line, which means a higher rate of change. For example, a slope of 6.5 means the function increases more rapidly than a slope of 2.

Front

How can you identify the greater y-intercept between two linear functions?

Back

To identify the greater y-intercept, compare the values of b in the equations of the two functions. The function with the higher b value has the greater y-intercept.

Front

What does it mean for a function to have a negative slope?

Back

A negative slope indicates that as the value of x increases, the value of y decreases. The line slopes downward from left to right.

Front

How do you graph a linear function?

Back

To graph a linear function, start by plotting the y-intercept on the y-axis. Then use the slope to determine another point on the line, and draw a straight line through the points.

Front

What is the formula for calculating the slope between two points?

Back

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).