Slope, Point-Slope and Standard Form Review

Front

What is the definition of slope in a linear equation?

Back

Slope is a measure of the steepness of a line, typically represented as 'm' in the equation of a line. It is calculated as the change in y divided by the change in x (rise/run).

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 point-slope form of a linear equation?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What does it mean if the slope of a line is positive?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does it mean if the slope of a line is negative?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero in the slope formula.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y as x changes.

Front

How do you find the y-intercept of a line given its equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the y-intercept is the value of b, which is the point where the line crosses the y-axis.