Linear Equations forms

Front

What is the formula for calculating the slope (m) 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 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 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

How do you convert the standard form of a linear equation Ax + By = C to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line descends from left to right, meaning as x increases, y decreases.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.

Front

Given the points (2, 3) and (4, 7), calculate the slope of the line that passes through these points.

Back

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

Front

What is the significance of the slope being zero?

Back

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

Front

What is the significance of a vertical line in terms of slope?

Back

A vertical line has an undefined slope because the change in x is zero, leading to division by zero in the slope formula.