Slope and Slope Intercept

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the rise (change in y) over the run (change in x).

Front

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

Back

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

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 does a zero slope indicate?

Back

A zero slope 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 while y changes.

Front

How do you find the y-intercept from the equation 2x + 3y = 6?

Back

To find the y-intercept, set x = 0. The equation becomes 3y = 6, so y = 2. The y-intercept is (0, 2).

Front

What is the x-intercept of the equation 4x + 2y = 8?

Back

To find the x-intercept, set y = 0. The equation becomes 4x = 8, so x = 2. The x-intercept is (2, 0).

Front

What is the slope of the line represented by the equation y = 5x + 1?

Back

The slope of the line is 5.

Front

What is the y-intercept of the line represented by the equation y = -3x + 4?

Back

The y-intercept of the line is (0, 4).