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Draw the graph for the following equations graph:?

0 votes
i) 5x - 8y + 1 = 0, 3x - (24/5)y + 3/5 = 0
(ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0
(iii) 6x - 3y + 10 = 0, 2x - y + 9 = 0.
asked Jun 18, 2014 in CALCULUS by anonymous

3 Answers

0 votes

i) The equations are image

Write the equations in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

  • First equation is 5x - 8y + 1 = 0

-8y = -1 - 5x

y = - 5x/-8 - 1/-8

y = 5x/8 + 0.125

  • Second equation image

image

 image

image

y = 5x/8 + 0.125

Observe the two lines are equal.

y = 5x/8 + 0.125

Compare the equation with slope-intercept form y = mx + b.

slope = 5/8 and y-intercept is 0.125.

y-intercept is 0.125, so the line crosses the y-axis at (0, 0.125)

Using slope find the next point.

Slope = rise/run = 5/8

Start at point (0, 0.125), move 5 units up and 8 units right, then plot the point (8, 5.125).

Draw a line through these points.

Graph :

graph for the equation - x - 2y = 8

 

answered Jun 18, 2014 by david Expert
edited Jun 18, 2014 by david
0 votes

(ii).

Graph by using intercepts:

The system of equations are 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0.

Divide equation : 18x + 6y + 24 = 0 by  2.

9x + 3y + 12 = 0.

So, given two lines are equal lines.

  • Find the x - intercept :

Find the x - intercept by substiting y = 0 in 9x + 3y + 12 = 0.

9x + 3(0) + 12 = 0

9x + 12 = 0

9x = - 12

x = - 12/9

⇒ x = - 4/3.

The x - intercept is - 4/3, so the line crosses the x - axis at (- 4/3, 0).

  • Find the y - intercept :

Find the y - intercept by substiting x = 0 in 9x + 3y + 12 = 0.

9(0) + 3y + 12 = 0

3y + 12 = 0

3y = - 12

y = - 12/3

⇒ y = - 4.

The y - intercept is - 4, so the line crosses the y - axis at (0, - 4).

  • Draw a coordinate plane.
  • Plot the x and y intercept points.
  • Draw a line through these points.

Graph :

answered Jun 18, 2014 by lilly Expert
0 votes

Graph by making a Table.

(iii) The equations are 6x - 3y + 10 = 0 and 2x - y + 9 = 0

Write the equations in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

  • First equation 6x - 3y + 10 = 0

6x + 10 = 3y

y = 6x/3 + 10/3

y = 2x + 10/3

The domain is all real numbers .Select values from the domain and make a table. Create orderd pairs and graph them.

y

 y = 2x + 10/3

(x, y )

 1

y = 2(1) + 10/3 = 16/3

 (1,16/3)  

-1

y = 2(-1) + 10/3  = 4/3

(-1, 4/3)

2

y = 2(2) + 10/3 = 22/3

(2, 22/3)

-2

y = 2(-2) + 10/3 = -2/3

(-2, -2/3)

  • Second equation 2x - y + 9 = 0

y =  2x + 9

The domain is all real numbers .Select values from the domain and make a table. Create orderd pairs and graph them.

y

 y = 2x + 9

(x, y )

 1

y = 2(1) + 9 = 11

 (1, 11)  

-1

y = 2(-1) + 9 = 7

(-1, 7)

0

y = 2(0) + 9 = 9

(0, 9)

-3

y = 2(-3) + 9 = 3

(-3, 3)

Graph

1) Draw the coordinate plane.

2) Plot the points of two lines.

3) Connect the plotted points.

From the graph we observe the lines are parallel.

answered Jun 18, 2014 by david Expert
edited Jun 18, 2014 by david

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