A1.2.2.1.4 Linear Equations and Graphs

Front

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

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent?

Back

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

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 is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form is given by Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean if a line has a slope of 0?

Back

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

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, meaning there is no change in x as y changes.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.