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Lesson 6-3 (Part 1) Standard Form page 298PowerPoint Presentation

Lesson 6-3 (Part 1) Standard Form page 298

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### Lesson 6-3 (Part 1)Standard Formpage 298

Objective: To graph equations using intercepts.

Real-World Connection

- We can use an equation to model a situation that involves exercise, as in example 5.

DEFINITION

- Standard form of a linear equation:
Ax + By = C

where A, B, and C are real numbers and

A and B are not zero.

x-intercept—the x-coordinate of the point where a line crosses the x-axis

y-intercept– the y-coordinate of the point where a

line crosses the y-axis

Find the x- and y-intercepts of 2x + 5y = 6.

Step 2 To find the y-intercept,

substitute 0 for x and

solve for y.

2x + 5y = 6

2(0) + 5y = 6

5y = 6

y =

The y-intercept is .

6

5

6

5

Standard FormALGEBRA 1 LESSON 6-3

Step 1 To find the x-intercept, substitute 0 for y and

solve for x.

2x + 5y = 6 2x + 5(0) = 6 2x = 6 x = 3

The x-intercept is 3.

6-3

Graphing Using Intercepts

- Find the x-intercept by substituting zeros for y.
- Find the y-intercept by substituting zeros for x.
- Plot the intercepts.
- Draw the line.

Graph 3x + 5y = 15 using intercepts.

Step 2 Plot (5, 0) and (0, 3).

Draw a line through the points.

Standard FormALGEBRA 1 LESSON 6-3

Step 1 Find the intercepts.

3x + 5y = 15

3x + 5(0) = 15 Substitute 0 for y.

3x = 15 Solve for x.

x = 5

3x + 5y = 15

3(0) + 5y = 15 Substitute 0 for x.

5y = 15 Solve for y.

y = 3

6-3

Special Lines

In standard form

Ax + By = C

either A or B = 0, but not both.

- If A = 0, the line is horizontal and the equation looks like: y = #.
- If B = 0, the line is vertical and the equation looks like: x = #.

Standard Form

ALGEBRA 1 LESSON 6-3

a. Graph y = 4

b. Graph x = –3.

0 • x + 1 • y = 4 Write in standard form.

For all values of x, y = 4.

1 • x + 0 • y = –3 Write in standard form.

For all values of y, x = –3.

6-3

Summary

- What did you learn today?

SUMMARY

- Standard form of an equation is
Ax + By = C

- A horizontal line has equation y = #.
- A vertical line has equation x = #.

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