Linear Functions (slope intercept form; point slope form)

Front

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

Back

The slope-intercept form is given by the equation 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 represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

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

Back

The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

What does a positive slope indicate about a line?

Back

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

Front

What is the y-intercept 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 slope-intercept form.

Front

How can you convert from slope-intercept form to point-slope form?

Back

To convert, identify the slope (m) and y-intercept (b) from y = mx + b, then use a point (0, b) in the point-slope form.

Front

What is the relationship between the slope and the rate of change?

Back

The slope of a line is equivalent to the rate of change; it quantifies how much y changes for a unit change in x.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that y does not change as x changes.