Standard form - intercepts

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 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 intercepts in the context of a linear equation?

Back

Intercepts are the points where the line crosses the x-axis (x-intercept) and y-axis (y-intercept).

Front

What is the x-intercept of the equation 2x + y = 6?

Back

The x-intercept is (3, 0).

Front

What is the y-intercept of the equation 2x + y = 6?

Back

The y-intercept is (0, 6).

Front

How do you determine the slope of a line from its equation?

Back

The slope can be determined from the equation in slope-intercept form (y = mx + b), where m is the slope.

Front

What is the slope of the line represented by the equation 2x + y = 6?

Back

The slope is -2.

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How can you convert the equation 4x + 2y = -12 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = -2x - 6.