HW Standard Form- Linear Equations

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 do you find the x-intercept of a linear equation?

Back

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

Front

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

Back

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

Front

What are the x- and y-intercepts of the equation 2x + 5y = -10?

Back

The x-intercept is (-5, 0) and the y-intercept is (0, -2).

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope of the line represented by the equation 2x + 4y = 14?

Back

The slope can be found by rearranging the equation to slope-intercept form, yielding a slope of -1/2.

Front

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

Back

A and B determine the orientation and steepness of the line; A affects the x-direction and B affects the y-direction.

Front

How do you graph a linear equation in standard form?

Back

To graph a linear equation in standard form, find the x- and y-intercepts, plot them, and draw a line through these points.

Front

What is the relationship between parallel lines in terms of their slopes?

Back

Parallel lines have the same slope but different y-intercepts.