Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept (b) in the slope-intercept form of a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

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

Back

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

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, and A should be non-negative.

Front

How can you determine if two lines are parallel?

Back

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

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning one slope is the negative reciprocal of the other.

Front

What is the significance of the graph of a linear equation?

Back

The graph of a linear equation visually represents the relationship between the variables x and y, showing all possible solutions to the equation.

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 (y = mx + b), solve for y in terms of x.

Front

What is the relationship between the slope and the steepness of a line?

Back

The greater the absolute value of the slope, the steeper the line. A positive slope rises to the right, while a negative slope falls to the right.