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 convert the equation y = mx + b to standard form?

Back

To convert y = mx + b to standard form, rearrange the equation to the form Ax + By = C by moving all terms involving x and y to one side.

Front

What does the slope (m) represent in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How can you find the x-intercept of a linear equation in standard form?

Back

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

Front

How can you find the y-intercept of a linear equation in standard form?

Back

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

Front

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

Back

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

Front

Graph the equation 2x + 4y = 4. What are the intercepts?

Back

The x-intercept is (2, 0) and the y-intercept is (0, 1).

Front

Graph the equation -x + 2y = 3. What are the intercepts?

Back

The x-intercept is (-3, 0) and the y-intercept is (0, 1.5).

Front

Which graph represents the equation 2x + 4y = 12?

Back

The graph will show a line that intersects the x-axis at (6, 0) and the y-axis at (0, 3).