Write Linear Equations in Standard Form

Section 5.4

P. 311 - 314

• In this section you will review the Standard Form of a linear equation.

• Understand how write equivalent equations in standard form

• You will take an equation in the Slope-Intercept Form and put it correctly in the Standard Form

• Do you recall that the linear equation Ax + By = C is in standard form,

• where A, B, & C are Real numbers and A & B are not both zero.

To write another equivalent equation, multiply each side by 0.5.

4x – 12y = 8

To write one equivalent equation, multiply each side by 2.

SOLUTION

Write two equations in standard form that are equivalent to 2x – 6y = 4.

EXAMPLE 1 Write equivalent equations in standard form

x – 3y = 2

EXAMPLE 1GUIDED PRACTICE for Examples 1 and 2

Write two equations in standard form that are equivalent to x – y = 3.

1.

2x – 2y = 6, 3x – 3y = 9ANSWER

EXAMPLE 2 Write an equation from a graphGUIDED PRACTICE for Examples 1 and 2

Write an equation in standard form of the line through (3, –1) and (2, –3).

2.

–2x + y = –7ANSWER

SOLUTION

Calculate the slope.STEP 1

EXAMPLE 2 Write an equation from a graph

–3m =1 – (–2)

1 – 2=

3–1 =

Write an equation in standard form of the line shown.

SOLUTION

EXAMPLE 3 Write an equation of a line

Write an equation of the specified line.

The y-coordinate of the given point on the blue line is –4. This means that all points on the line have a y-coordinate of –4. An equation of the line is y = –4.

a.

The x-coordinate of the given point on the red line is 4. This means that all points on the line have an x-coordinate of 4. An equation of the line is x = 4.

b.

Blue linea. Red lineb.

Write equations of the horizontal and vertical lines that pass through the given point.

GUIDED PRACTICE for Examples 3 and 4

3. (–8, –9)

y = –9, x = –8ANSWER

GUIDED PRACTICE for Examples 3 and 4

4. (13, –5)

y = –5, x = 13ANSWER

Write equations of the horizontal and vertical lines that pass through the given point.

Simplify.

Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A.

STEP 1

SOLUTION

EXAMPLE 4

Find the missing coefficient in the equation of the line shown. Write the completed equation.

Ax + 3y = 2A(–1) + 3(0) = 2

–A = 2A = –2

Write equation.

Substitute –1 for x and 0 for y.

Divide by –1.

EXAMPLE 3EXAMPLE 4Complete an equation in standard form

EXAMPLE 4Complete an equation in standard form

Complete the equation.

–2x + 3y = 2 Substitute –2 for A.

STEP 2

EXAMPLE 4Complete an equation in standard form

Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.

EXAMPLE 3 Write an equation of a lineGUIDED PRACTICE for Examples 3 and 4

5. –4x + By = 7, (–1, 1)

ANSWER 3; –4x + 3y = 7

• Assignment: P. 314 5-6, 11-19, 23-25, 30