Unit 3 Linear Functions LPC Redo

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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line 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

How do you find the y-intercept of a linear function?

Back

The y-intercept of a linear function is found by setting x = 0 in the equation of the line and solving for y.

Front

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

Back

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

Front

What is the significance of the y-intercept in a linear function?

Back

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

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the rate of change (slope) between any two points is constant.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the value of x increases, the value of y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, resulting in a downward slant of the line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph a linear function using its slope and y-intercept?

Back

To graph a linear function, plot the y-intercept on the y-axis, then use the slope to determine the rise over run to find another point on the line.