Changing 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 it mean to change the form of a linear equation?

Back

Changing the form of a linear equation means rewriting it in a different format, such as from slope-intercept form (y = mx + b) to standard form (Ax + By = C).

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing a linear equation as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is standard form of a linear equation?

Back

Standard form of a linear equation is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side and set it equal to a constant.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form (y = mx + b).

Front

How can you identify the slope from a linear equation in standard form?

Back

In standard form (Ax + By = C), the slope can be found by rearranging the equation into slope-intercept form (y = mx + b) and identifying the coefficient of x.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and the y-intercept, which define the line's steepness and where it crosses the y-axis.

Front

What is a parallel line in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts. They never intersect.