Slope / Slope-intercept form

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope 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 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 y-intercept represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

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 while y changes.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

How do you find the slope of a line given its equation in standard form Ax + By = C?

Back

Rearrange the equation to slope-intercept form (y = mx + b) to identify the slope (m) as -A/B.

Front

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

Back

The slope of the line is -3.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.