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 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 and the direction it goes (positive or negative).

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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

What does it mean if the slope is zero?

Back

If the slope is zero, it means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does it mean if the slope is undefined?

Back

If the slope is undefined, it means the line is vertical, indicating that there is no change in x as y changes.

Front

How can you determine if a linear equation is increasing or decreasing?

Back

A linear equation is increasing if the slope (m) is positive and decreasing if the slope (m) is negative.

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 slope of 2 is steeper than a slope of 1.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept (b), plot it on the y-axis, and use the slope (m) to find another point on the line.