4.5 - Standard Form of a Linear Equations

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 and B are not both zero.

Front

How do you find the y-intercept of a linear equation?

Back

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

Front

What is the y-intercept of the equation 2x - 5y = 35?

Back

(0, -7)

Front

How do you find the x-intercept of a linear equation?

Back

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

Front

What is the x-intercept of the equation 3x + 8y = 24?

Back

(8, 0)

Front

What does the slope of a line represent?

Back

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

Front

How can you convert the equation 4x + 2y = -12 to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y: y = -2x - 6.

Front

What is the slope of the line represented by the equation 2x + 4y = 12?

Back

The slope is -1/2.

Front

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

Back

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

Front

How do you graph a linear equation in standard form?

Back

Find the x-intercept and y-intercept, plot these points, and draw a line through them.