Linear Functions

Front

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

Back

The point-slope form of a linear equation is given by: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you find the slope of a line given two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).

Front

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

Back

The slope-intercept form is given by: y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant regardless of the value of y.

Front

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

Back

To convert, solve for y in the point-slope form equation: y - y_1 = m(x - x_1) to get y = mx + b.

Front

What is the formula for the slope of a line that passes through the points (0, b) and (x, mx + b)?

Back

The slope (m) is calculated as m = (mx + b - b) / (x - 0) = m.

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y_1 = m(x - x_1), substituting the point (x_1, y_1) and the slope m.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope; if two lines are parallel, their slopes (m) are equal.