Algebra IA - Standard Form of a Linear Equation

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 y-intercept of a linear equation?

Back

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

Front

What is the y-intercept of the equation 2x + 3y = 6?

Back

The y-intercept is (0, 2) after solving for y when x = 0.

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

What is the x-intercept of the equation 3x + 4y = 12?

Back

The x-intercept is (4, 0) after solving for x when y = 0.

Front

What does it mean for an equation to be in standard form?

Back

An equation is in standard form if it is written as Ax + By = C, where A, B, and C are integers.

Front

Which of the following is NOT in standard form: 4x - 5y = 10 or 2y + 3 = 0?

Back

2y + 3 = 0 is not in standard form.

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 slope of the line; specifically, the slope is -A/B.

Front

How can you convert the equation y = 2x + 3 into standard form?

Back

Rearranging gives -2x + y = 3, which can be written as 2x - y = -3.

Front

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

Back

The x-intercept is the point where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.