5.3 Standard Form

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5.3 Standard Form. Objective : SWBAT find x- and y-intercepts and graph lines in standard form. Mini Quiz 42. Find the slope and y-intercept of Write an equation of a line with a slope m = 4 and y-intercept b = Determine whether the ordered pair (2, -7) lies on the graph y = -3 x – 1.

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### 5.3 Standard Form

Objective: SWBAT find x- and y-intercepts and graph lines in standard form.

Mini Quiz 42
• Find the slope and y-intercept of
• Write an equation of a line with a slope

m = 4 and y-intercept b =

• Determine whether the ordered pair (2, -7) lies on the graph y = -3x – 1
Quick Review
• What is the Slope Formula?
• What is the Slope-Intercept Form?

y = mx + b

• How do you check if a point is on the line?

Plug it in! If it’s =, it’s on the line

• How do you find rate of change?

Take the independent “over” the dependent

Overview
• Learn about the standard form
• Finding x- and y- intercepts with standard form
• Graphing Lines Using Intercepts
• Graphing Horizontal and Vertical Lines
• Transforming to Standard Form

So far, we have learned slope-intercept

form…

y = mx + b

Standard Form

Ax +By =C

A, B, and C are integers

Examples:

2x + 5y = 6

x – 3y = -7

x- and y-intercepts
• How do you write the ordered pair of any point on the x-axis?

(x, 0)

• How do you write the ordered pair of any point on the y-axis?

(0, y)

Find the x- and y-intercepts

1. 2x + 6y = 36

How do you write the ordered pair for a point on the x-axis?

(x, 0) – replace the “0” for y

2x + 6(0) = 36

2x = 36

x = 18 (18, 0)

How do you write the ordered pair for a point on the y-axis?

(0, y) – replace the “0” for x

2(0) + 6y = 36

6y = 36

y = 6 (0, 6)

Find the x- and y-intercepts

2. -3x + 2y = -12

How do you write the ordered pair for a point on the x-axis?

(x, 0) -replace the “0” for y

-3x + 2(0) = -12

-3x = -12

x = 4 (4, 0)

How do you write the ordered pair for a point on the y-axis?

(0, y) – replace the “0” for x

-3(0) + 2y = -12

2y = -12

y = -6 (0, -6)

Find the x- and y-intercepts

3. -2x – 3y = -8

How do you write the ordered pair for a point on the x-axis?

(x, 0)

-2x – 3(0) = -8

-2x = -8

x = 4 (4, 0)

How do you write the ordered pair for a point on the y-axis?

(0, y)

-2(0) – 3y = -8

-3y = -8

y = 8/3 (0, 8/3)

Find the x- and y-intercepts

4. 8x – 3y = 17

How do you write the ordered pair for a point on the x-axis?

(x, 0)

8x – 3(0) = 17

8x = 17

x = 17/8 (17/8, 0)

How do you write the ordered pair for a point on the y-axis?

(0, y)

8(0) – 3y = 17

-3y = 17

y = -17/3 (0, -17/3)

Graph by using the x- and y-intercepts

5. 3x + 4y = 24

• How do you write the ordered pair for a point on the x-axis?

(x, 0)

3x = 24

x = 8

(8, 0)

• How do you write the ordered pair for a point on the y-axis?

(0, y)

4y = 24

y = 6

(0, 6)

Graph by using the x- and y-intercepts

6. -3x – 2y = -6

• How do you write the ordered pair for a point on the x-axis?

(x, 0)

-3x = -6

x = 2

(2, 0)

• How do you write the ordered pair for a point on the y-axis?

(0, y)

-2y = -6

y = 3

(0, 3)

Graph by using the x- and y-intercepts

7. -2x + 3y = -18

• How do you write the ordered pair for a point on the x-axis?

(x, 0)

-2x = -18

x = 9

(9, 0)

• How do you write the ordered pair for a point on the y-axis?

(0, y)

3y = -18

y = -6

(0, -6)

Graph by using the x- and y-intercepts

8. x + 4y = -8

• How do you write the ordered pair for a point on the x-axis?

(x, 0)

x = -8

(-8, 0)

• How do you write the ordered pair for a point on the y-axis?

(0, y)

4y = -8

y = -2

(0, -2)

Graphing Horizontal and Vertical Lines
• 10. y = -4
• 12. y = 2
• x = 3

11. x = -4

Change to Standard Form
• Write in standard form

-3x + 4y = 8

14. Write in standard form

2x + 5y = 5

Wrap Up
• Standard Form
• Ax + By = C
• Finding and Graphing x- and y-intercepts
• Horizontal and Vertical Lines
• Change to Standard

HW: P. 249 #1-61 EOO,

69 – 77 odd

DLUQ: How do you find the x- and y-intercepts