Representations of Linear Functions

Front

What is the general form of a linear function?

Back

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

Front

How do you determine the slope of a linear function from a graph?

Back

The slope of a linear function can be determined by finding the rise over run between two points on the line.

Front

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

Back

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

Front

How can you write an equation for a linear function given a slope and a point?

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is slope-intercept form of a linear equation?

Back

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

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

Back

The slope indicates the rate of change of y with respect to x; it shows how much y increases or decreases as x increases.

Front

How do you find the equation of a line given two points?

Back

First, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), then use point-slope form to write the equation.

Front

What does a positive slope indicate about a linear function?

Back

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