3.8b Rearranging Equations

Front

What is the process of rearranging equations?

Back

Rearranging equations involves manipulating the equation to isolate a variable on one side, making it easier to solve for that variable.

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 convert from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving variables on one side and the constant on the other.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means to manipulate an equation so that the variable is alone on one side of the equation.

Front

Given the equation 6x + y = 10, what is y in terms of x?

Back

y = -6x + 10.

Front

What is the slope-intercept form of the equation y - 7 = -2/3(x + 1)?

Back

y = -2/3x + 5/3.

Front

How do you find the slope of a line from an equation in standard form?

Back

The slope (m) can be found using the formula m = -A/B from the standard form Ax + By = C.

Front

What is the slope of the line represented by the equation 2x - 5y = 15?

Back

The slope is 2/5.

Front

How do you convert the equation y = (-1/4)x - 4 to standard form?

Back

Multiply by -4 to get 4y + x = -16, or rearrange to x + 4y = -16.

Front

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

Back

In slope-intercept form (y = mx + b), m represents the slope and b represents the y-intercept.