Flashcard - Equation of Straight Lines

Front

What is the general form of the equation of a straight line?

Back

The general form of the equation of a straight line is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you find the slope (gradient) 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 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 can you determine the y-intercept of a line from its equation?

Back

The y-intercept can be determined from the equation in slope-intercept form (y = mx + b) as the value of b.

Front

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

Back

The slope of a line 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 0, what does that indicate about the line?

Back

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

Front

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

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How do you write the equation of a line given a point and a slope?

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

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

Back

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

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).