Linear Equations in Standard Form

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 and B are not both zero.

Front

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

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the slope of a line in standard form?

Back

The slope (m) can be found using the formula m = -A/B from the standard form Ax + By = C.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, which occurs when the equation is of the form x = a.

Front

How do you find the x-intercept of a linear equation in standard form?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the significance of the coefficients A and B in the standard form of a linear equation?

Back

The coefficients A and B determine the slope and direction of the line.

Front

What is the relationship between the slope and the y-intercept in a linear equation?

Back

The slope indicates the steepness of the line, while the y-intercept is the point where the line crosses the y-axis.

Front

How can you convert a linear equation from standard form to slope-intercept form?

Back

To convert, solve for y to get the equation in the form y = mx + b.

Front

What is the y-intercept of the equation 3x + y = 5?

Back

The y-intercept is (0, 5).

Front

What are the x- and y-intercepts of the equation 2x + y = 6?

Back

The x-intercept is (3, 0) and the y-intercept is (0, 6).