Standard Form and Graphs

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 the equation 2y = 4x + 8 into standard form?

Back

To convert to standard form, rearrange to get -4x + 2y = 8, or 4x - 2y = -8.

Front

What is the first step to graph a linear equation in standard form?

Back

The first step is to find the x-intercept and y-intercept by setting y=0 and x=0 respectively.

Front

What does the slope-intercept form of a line look like?

Back

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

Front

How can you identify the slope from the standard form equation 3x + 4y = 12?

Back

Rearranging to slope-intercept form gives y = -3/4x + 3, so the slope is -3/4.

Front

What is the significance of the coefficients A, B, and C in the standard form Ax + By = C?

Back

A and B determine the slope of the line, while C represents the point where the line intersects the axes.

Front

What is the x-intercept of the equation 5x + 2y = -12?

Back

To find the x-intercept, set y=0: 5x = -12, so x = -12/5.

Front

What is the y-intercept of the equation 5x + 4y = 4?

Back

To find the y-intercept, set x=0: 4y = 4, so y = 1.

Front

How do you graph the equation x - 4y = 3?

Back

Find the intercepts: x-intercept (3,0) and y-intercept (0,-3/4), then plot and draw the line.

Front

What is the standard form of the equation for a line with slope 2 and y-intercept -3?

Back

The standard form is 2x - y = 3.