Graph Standard Form Practice

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

Front

What are x- and y-intercepts?

Back

The x-intercept is the point where a line crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

Given the equation 3x + y = 5, what is the y-intercept?

Back

The y-intercept is (0, 5).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

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

Back

The slope (m) 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 convert the standard form of a linear equation to slope-intercept form?

Back

To convert Ax + By = C to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

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

Back

The coefficient of x represents the slope (m), and the constant term represents the y-intercept (b) in the slope-intercept form.