3.5 Standard Form

Front

What is Standard Form in linear equations?

Back

Standard Form is a way of writing linear equations in the format Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you find the y-intercept from a standard form equation?

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

The slope is -2/3, found by rearranging to slope-intercept form.

Front

What does the term 'intercept' mean in the context of a graph?

Back

An intercept is a point where a line crosses an axis; the y-intercept is where it crosses the y-axis.

Front

Convert the equation 4x - 2y = 8 to slope-intercept form.

Back

y = 2x - 4.

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, and if B = 0, the line is vertical.

Front

How do 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 y-intercept of the equation 3x - 4y = 12?

Back

The y-intercept is (0, -3).

Front

What is the slope of the line represented by the equation 5x + 2y = 10?

Back

The slope is -5/2.