Graphing 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 find the x-intercept of the equation 2x + y = 6?

Back

To find the x-intercept, set y = 0. The equation becomes 2x + 0 = 6, so x = 3. The x-intercept is (3, 0).

Front

How do you find the y-intercept of the equation 2x + y = 6?

Back

To find the y-intercept, set x = 0. The equation becomes 2(0) + y = 6, so y = 6. The y-intercept is (0, 6).

Front

What do the x- and y-intercepts represent in a graph?

Back

The x-intercept represents the point where the graph crosses the x-axis, and the y-intercept represents the point where the graph crosses the y-axis.

Front

What is the slope of a line in standard form?

Back

The slope of a line in standard form Ax + By = C can be found by rearranging it to slope-intercept form (y = mx + b), where m is the slope.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the significance of the equation -7x + 2y = 9 being in standard form?

Back

It is in standard form because it can be easily manipulated to find intercepts and slope, and it follows the format Ax + By = C.

Front

How can you convert the equation y - 3 = -5(x + 2) to standard form?

Back

Distribute and rearrange: y - 3 = -5x - 10 becomes 5x + y = -7.

Front

What is the x-intercept of the equation 3x + 2y = 12?

Back

Set y = 0: 3x + 0 = 12, so x = 4. The x-intercept is (4, 0).