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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Standard Form of a Line

If x students paid \$5 each and y adults paid \$7 each to attend a play for which the ticket sales totaled \$1900, then we can write the equation 5x + 7y = 1900. This form of a linear equation is common in applications. It is called standard form.

Standard Form

The equation of a line in standard form is Ax + By = C, where A, B, and C are real numbers with A and B not both zero.

The numbers A, B, and C in standard form can be any real numbers, but it is a common practice to write standard form using only integers and a positive coefficient for x.

Example 1

Changing to standard form

Write the equation in standard form using only integers and a positive coefficient for x.

Solution

Use the properties of equality to get the equation in the form Ax + By = C:

 y Original equation Subtract from each side. Multiply each side by 4 to get integral coefficients. -2x + 4y = -3 Distributive property 2x - 4y = 3 Multiply by -1 to make the coefficient of x positive.

To find the slope and y-intercept of a line written in standard form, we convert the equation to slope-intercept form.

Example 2

Changing to slope-intercept form

Find the slope and y-intercept of the line 3x - 2y = 5.

Solution

Solve for y to get slope-intercept form:

 3x - 2y = 5 Original equation -2y = -3x + 5 Subtract 3x from each side. y Divide each side by -2.

The slope is , and the y-intercept is .