Writing Equations in Standard Form

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 point-slope form to standard form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to standard form, rearrange the equation to isolate the variables on one side and constants on the other.

Front

What is 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

How do you convert from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form, rearrange the equation to the form Ax + By = C.

Front

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

Back

An equation is in standard form when it is expressed as Ax + By = C, with A, B, and C being integers and A being non-negative.

Front

What is the significance of the coefficients A and B in standard form?

Back

The coefficients A and B determine the slope of the line and its orientation in the coordinate plane.

Front

How can you identify the slope from a standard form equation?

Back

The slope can be identified from a standard form equation Ax + By = C by rearranging it into slope-intercept form (y = mx + b) and finding the value of m.

Front

What is the first step in converting a point-slope equation to standard form?

Back

The first step is to distribute the slope (m) across the parentheses in the point-slope equation.

Front

What is the relationship between slope-intercept form and standard form?

Back

Both forms represent linear equations, but slope-intercept form emphasizes the slope and y-intercept, while standard form emphasizes integer coefficients.

Front

Can standard form equations have fractions?

Back

No, standard form equations should have integer coefficients. If fractions are present, multiply through by the denominator to eliminate them.