Equation of a Straight Line

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# Equation of a Straight Line - PowerPoint PPT Presentation

Equation of a Straight Line. Investigation. y = 2x +1. Fill in table. Write points as coordinates. Draw a coordinates grid and plot points. Draw a line through points. Use your two coordinates to calculate gradient. From your diagram find where the line cuts the Y axis .

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### Equation of a Straight Line

Investigation

y = 2x +1

Fill in table

Write points as coordinates

Draw a coordinates grid and plot points

Draw a line through points

Use your two coordinates to calculate gradient

From your diagram find where the line cuts the Y axis

(the y intercept!)

Repeat for y = 3x – 2

Fill in table

Write points as coordinates

Draw a coordinates grid and plot points

Draw a line through points

Use your two coordinates to calculate gradient

From your diagram find where the line cuts the Y axis

(the y intercept!)

Also

y = -2x + 4

y = ½ x – 3

m

Y Intercept

(0 , 1)

y = 2x + 1

2

(0 , -2)

y = 3x – 2

3

(0 , 4)

y = -2x + 4

-2

(0 , -3)

y = ½ x – 3

½

Equation is related to:
• Y intercept (cuts Y axis)

y

(0 ,…)

x

3

(0 , 5)

- ½

(0 , 7)

Y = 3x + 5

Y = - ½ x + 7

3

(0 , 5)

- ½

(0 , 7)

Y = 3x + 5

Y = - ½ x + 7

3

(0 , 5)

- ½

(0 , 7)

Y = 3x + 5

Y = - ½ x + 7

Y =8x – 5

Y = -6x + 9

(0, -5)

8

(0, 9)

-6

Equation of a Straight Line

Is in form

y = mx + c

Ex 1 y = - ¾ x + 2

m = - ¾ , y int (0 , 2)

Ex 2 m = 9, y int (0 , -8)

y = 9x - 8

Y intercept (0 ,?)

Write down gradient and Y intercept

1. y = 2x + 4

2. y = ½ x -7

3. y = -5x + 6

4. y = x + 8

5. y = 7x

6. y = 6 + 2x (careful)

7. y = 9 – 3x

8. y = 7

Write down the equation

m Y intercept

1. 5 (0 , 7)

2. -5 (0 , 5)

3. ¾ (0 , -6)

4. -5 (0 , -5)

5. 1 (0 , 4)

6. 8 (0 , 0)

7. 0 (0 , 9)

Calculating equation

y

Need 2 points

(1 , 2)

m = 2 – (-1)

1 - 0

m

(x2, y2)

c

= 3/1 = 3

x

(0 , -1)

y intercept

-1

(x1, y1)

Equation y = 3x - 1

Calculating equation

y

(-2 , 3)

(x1, y1)

Need 2 points

(2 , 1)

m = 1 – 3

2 – (-2)

m

(x2, y2)

c

= -2/4 = - ½

x

y intercept

2

Equation y = - ½ x + 2

Special Cases

y

(0 , 4)

(annoying lines!)

Horizontal lines

Y = 0x + 4

Y = 4

m = 0

x

Special Cases

No y intercept!

y

Vertical lines

(really annoying!)

(2 , 4)

m = ∞

x

(2 , 0)

(2 , -2)

Special Cases

No y intercept!

y

Vertical lines

(really annoying!)

(2 , 4)

m = ∞

x

(2 , 0)

(2 , -2)

Equation x = 2

Annoying Lines Equations

Horizontal Lines (m = 0)

are in form y = ? (i.e no x)

Vertical lines (m = ∞)

are in form x = ? (i.e no y)

y

Y = 5

(0 , 5)

(7 , 0)

x

X = 7