Converting Linear Equations between forms

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

Identify the slope-intercept form of a linear equation.

Back

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

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

How do you convert 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 y-intercept in the equation y = 2x + 3?

Back

The y-intercept is 3, which is the value of y when x = 0.

Front

How can you determine if an equation is in standard form?

Back

An equation is in standard form if it can be expressed as Ax + By = C, with A, B, and C as integers.

Front

What is the slope of the line represented by the equation y = -4x + 5?

Back

The slope of the line is -4.

Front

Convert the equation 3x - 2y = 6 to slope-intercept form.

Back

The slope-intercept form is y = (3/2)x - 3.

Front

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

Back

The coefficients A and B determine the slope and direction of the line, while C represents the line's position relative to the origin.

Front

Match the equation 4x + 3y = 12 to its slope-intercept form.

Back

The slope-intercept form is y = -4/3x + 4.