24-25 Fall Final Exam Review

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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 y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you determine if a point (x, y) lies on the line represented by the equation Ax + By = C?

Back

Substitute the x and y values into the equation. If the equation holds true, the point lies on the line.

Front

What is the significance of parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the significance of perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other (m1 * m2 = -1).

Front

How do you find the x-intercept of a line given its equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

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.

Front

How do you convert the equation of a line from standard form to slope-intercept form?

Back

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

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

The distance d is calculated using the formula d = √((x2 - x1)² + (y2 - y1)²).