Linear Equations Flashcard 1

Front

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

Back

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

Front

What does the slope of a line represent?

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

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

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 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 is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find at least two points that satisfy the equation and plot them on a coordinate plane, then draw a line through the points.

Front

What is the equation of a line with a slope of 0?

Back

The equation of a line with a slope of 0 is a horizontal line, represented as y = b, where b is the y-value.