Draw the graph for the following equations graph:?

Question

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.

Answer 1

i) The equations are

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

 

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 :

 

Answer 2

(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 :

Answer 3

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.