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

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

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Lesson 6 3 part 1 standard form page 298

Lesson 6-3 (Part 1)Standard Formpage 298

Objective: To graph equations using intercepts.


Real world connection

Real-World Connection

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


Definition

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


Standard form

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 Form

ALGEBRA 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


Example 1 page 299

Example 1, page 299

Find the x and y intercept of

3x + 4y = 8.


Example 1 page 2991

Example 1, page 299

Find the x-and y-intercepts of

4x – 9y = -12.


Graphing using intercepts

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.


Standard form1

Graph 3x + 5y = 15 using intercepts.

Step 2  Plot (5, 0) and (0, 3).

Draw a line through the points.

Standard Form

ALGEBRA 1 LESSON 6-3

Step 1 Find the intercepts.

3x + 5y = 15

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

3x = 15Solve for x.

x = 5

3x + 5y = 15

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

5y = 15Solve for y.

y = 3

6-3


Example 2 page 299

y

5

x

-5

5

-5

Example 2, page 299

  • Graph 2x + 3y = 12 using the

    x- and y-intercepts.


Example 2 page 2991

y

5

x

-5

5

-5

Example 2, page 299

  • Graph 5x + 2y = -10 using the

    x- and y-intercepts.


Special lines

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 form2

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


Example 3 page 299 graph each equation

y

y

5

5

x

x

-5

-5

5

5

-5

-5

Example 3, page 299Graph each equation.

  • a) y = -3b) x = 2


Example 3 page 299 graph each equation1

y

y

5

5

x

x

-5

-5

5

5

-5

-5

Example 3, page 299Graph each equation.

  • a) y = 5b) y = 0


Example 3 page 299 graph each equation2

y

y

5

5

x

x

-5

-5

5

5

-5

-5

Example 3, page 299Graph each equation.

  • c) x = -4d) x = 0


Summary

Summary

  • What did you learn today?


Summary1

SUMMARY

  • Standard form of an equation is

    Ax + By = C

  • A horizontal line has equation y = #.

  • A vertical line has equation x = #.


Assignment

ASSIGNMENT

Lesson 6-3 page 301

#1-26 all, 70-78 all


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