Linear Functions Flashcard

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line, which 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 line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is zero.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined.

Front

How do you calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in the equation of a line?

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

Convert the standard form equation 2x + 3y = 6 to slope-intercept form.

Back

The slope-intercept form is y = -2/3x + 2.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant from left to right.

Front

If a line has a slope of 4, what does this mean in terms of rise over run?

Back

A slope of 4 means that for every 1 unit you move to the right (run), the line rises 4 units (rise).