Slope & Slope-Intercept Form

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the rise over run between two points on the line.

Front

How is slope calculated?

Back

Slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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 the y-intercept represent in a linear equation?

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

Find the slope of the line passing through the points (2, 3) and (5, 9).

Back

Slope = (9 - 3) / (5 - 2) = 6 / 3 = 2.

Front

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

Back

A slope of 0 indicates a horizontal line, meaning there is no vertical change as x changes.

Front

If a line has an undefined slope, what does that indicate?

Back

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

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope is 4.

Front

How do you convert the equation 2x + 3y = 6 into slope-intercept form?

Back

Rearranging gives y = -2/3x + 2, so the slope is -2/3.

Front

What is the slope of the line represented by the equation y = -3x + 5?

Back

The slope is -3.