Standard Form of Linear Equations

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is represented as Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How do you find the y-intercept from the equation 2x - 5y = 35?

Back

To find the y-intercept, set x = 0. The equation becomes -5y = 35, so y = -7. The y-intercept is (0, -7).

Front

How do you convert the equation 2x + 8y = 24 to slope-intercept form?

Back

Rearranging gives y = -\frac{1}{4}x + 3.

Front

What is the x-intercept of the equation 3x + 8y = 24?

Back

To find the x-intercept, set y = 0. The equation becomes 3x = 24, so x = 8. The x-intercept is (8, 0).

Front

What is the y-intercept of the line 5x - 2y = 10?

Back

To find the y-intercept, set x = 0. The equation becomes -2y = 10, so y = -5. The y-intercept is (0, -5).

Front

What does the slope of a line represent?

Back

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

Front

What is the significance of the coefficients A and B in the standard form Ax + By = C?

Back

A and B determine the slope of the line. If A = 0, the line is horizontal; if B = 0, the line is vertical.

Front

How can you determine if two lines are parallel using their equations?

Back

Two lines are parallel if their slopes are equal. In standard form, convert to slope-intercept form to find the slopes.

Front

What is the relationship between the slope and the y-intercept in the slope-intercept form?

Back

In the slope-intercept form y = mx + b, m is the slope and b is the y-intercept, indicating where the line crosses the y-axis.