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

How do you find the y-intercept of a linear equation?

Back

The y-intercept is found by setting x to 0 in the equation and solving for y. It is the point where the line crosses the y-axis.

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 of a line is 0?

Back

If the slope of a line is 0, 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 of a line is undefined?

Back

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

Front

How can you determine the rate of change from a graph?

Back

The rate of change can be determined by calculating the slope of the line, which is the change in y divided by the change in x (rise/run).

Front

What is the relationship between the slope and the rate of change?

Back

The slope of a line is equivalent to the rate of change. A positive slope indicates a positive rate of change, while a negative slope indicates a negative rate of change.

Front

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

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 point-slope form of a linear equation?

Back

The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.