Writing linear equations CFA

Front

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

Back

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

Front

How do you calculate 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 does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

How can you determine if two points lie on the same line?

Back

Two points lie on the same line if the slope calculated between them is the same as the slope of the line.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

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

Front

What is the equation of a line that is vertical?

Back

The equation of a vertical line is of the form x = a, where a is the x-coordinate of any point on the line.

Front

What is the equation of a line that is horizontal?

Back

The equation of a horizontal line is of the form y = b, where b is the y-coordinate of any point on the line.

Front

How do you find the equation of a line given two points?

Back

First, calculate the slope using the two points, then use one of the points and the slope to write the equation in slope-intercept form.

Front

What is the relationship between the slopes of parallel and perpendicular lines?

Back

Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.