This document provides instructions on writing linear equations in standard form. It defines the standard form as Ax + By = C, where A, B, and C are real numbers and A and B are not both zero. Examples are provided of writing equivalent equations in standard form by multiplying both sides of an equation by a constant. The document also demonstrates writing the equation of a line given its slope and a point, or given just a single point. Students are guided in writing equations of horizontal and vertical lines and completing partial equations where a coefficient is missing. Practice problems are assigned for writing equations in standard form.

1. Write Linear Equations in
Standard Form
Section 5.4
P. 311 - 314

2. • 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

3. • 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.

4. EXAMPLE 1 Write equivalent equations in standard form
Write two equations in standard form that are equivalent
to 2x – 6y = 4.
SOLUTION
To write one equivalent To write another equivalent
equation, multiply each equation, multiply each side
side by 2. by 0.5.
4x – 12y = 8 x – 3y = 2

5. EXAMPLE 1
GUIDED PRACTICE for Examples 1 and 2
1. Write two equations in standard form that are
equivalent to x – y = 3.
ANSWER 2x – 2y = 6, 3x – 3y = 9

6. EXAMPLE 2 Write an equation from 1 and 2
GUIDED PRACTICE for Examples a graph
2. Write an equation in standard form of the line
through (3, –1) and (2, –3).
ANSWER –2x + y = –7

7. EXAMPLE 2 Write an equation from a graph
Write an equation in standard form of the line shown.
SOLUTION
STEP 1
Calculate the slope.
1 – (–2) 3
m= = –1 = –3
1–2

8. EXAMPLE 3 Write an equation of a line
Write an equation of the specified line.
a. Blue line b. Red line
SOLUTION
a. 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.
b. 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.

9. GUIDED PRACTICE for Examples 3 and 4
Write equations of the horizontal and vertical lines that
pass through the given point.
3. (–8, –9)
ANSWER y = –9, x = –8

10. GUIDED PRACTICE for Examples 3 and 4
Write equations of the horizontal and vertical lines that
pass through the given point.
4. (13, –5)
ANSWER y = –5, x = 13

11. EXAMPLE 4
3 Complete an equation in standard form
Find the missing coefficient in the equation of the line
shown. Write the completed equation.
SOLUTION
STEP 1
Find the value of A. Substitute the
coordinates of the given point for x and y in
the equation. Solve for A.
Ax + 3y = 2 Write equation.
A(–1) + 3(0) = 2 Substitute –1 for x and 0 for y.
–A = 2 Simplify.
A = –2 Divide by –1.

12. EXAMPLE 4 Complete an equation in standard form
STEP 2
Complete the equation.
–2x + 3y = 2 Substitute –2 for A.

13. GUIDED PRACTICE anan equation in line
EXAMPLE 4
3 Complete equation of and 4
Write for Examples 3 a standard form
Find the missing coefficient in the equation of the
line that passes through the given point. Write the
completed equation.
5. –4x + By = 7, (–1, 1)
ANSWER 3; –4x + 3y = 7

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