Question 1: Draw the graph of each of the following linear equations:

(i) x=0      (i) y=0      (iii) x+4=0      (iv) x-3=0      (v) y +2=0

(vi) y -7 = 0      (vii) 2y-3=0      (viii) 3x+7 =0      (ix) y=x      (x) y=-x

(xi) y = 2x      (xii) y=-3x      (xiii) 2y + 3x = 0      (xiv) 5y - 2x = 0

(xv) y =2x+5      (xvi) x+y+1=0      (xvii) x-y+4=0

(xviii) 2x + 3y - 12 = 0      (xix) 3x + 4y +24=0      (xx) 2x-3y +6=0

Answer:

i) to viii)

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ix) to xii)

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xiii) to xvi)

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xvii) to xx)

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Question 2: Find the slope and y-intercept of the lines represented by each of the following equations:     (i) 4x-3y+8=0     (ii) 2x+y-5=0               (iii) 5y+4=0    (iv) y = 2x     (v) 2x-3y =0

Answer:

For finding the slope and y-intercept, convert the equation into the form y = mx + c

i) 4x-3y+8=0

\Rightarrow 3y = 4x + 8

\Rightarrow y = \frac{4}{3} x + \frac{8}{3} 

\therefore  slope (m) = \frac{4}{3}   and  y-intercept = \frac{8}{3} 

(ii) 2x+y-5=0

\Rightarrow  y = -2x + 5

\therefore  slope (m) = -2   and  y-intercept = 5

(iii) 5y+4=0

\Rightarrow y = (0) x + \frac{-4}{5} 

\therefore  slope (m) = 0   and  y-intercept = \frac{-4}{5} 

(iv) y = 2x

\therefore  slope (m) = 2   and  y-intercept = 0

(v) 2x-3y =0 $

\Rightarrow 3y = 2x

\Rightarrow y = \frac{2}{3} x + 0

\therefore  slope (m) = \frac{2}{3}   and  y-intercept = 0

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Question 3: Draw the graph of the line represented by the equation 3x - 2y + 6 = 0 . Also, find the coordinates of the points where the line meets with the coordinate axes.

Answer:

To draw the line 3x - 2y + 6 = 0

x 0 -2
y 3 0

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Question 4: Draw the graphs of the lines represented by each of the following equations:     2x+3y=12 ,   x-y=1      Find the coordinates of the vertices  of the triangle formed by the two lines and the y-axis.

Answer:

To draw the line $latex 2x+3y=12

x 0 6
y 4 0

To draw the line $latex x-y=1

x 0 1
y -1 0

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Vertices of the triangle are (0, -1), (3, 2) \ \& \ (0, 4)

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Question 5: Draw the graphs of the following pairs of lines on the same graph paper and find their points of intersection. Are these lines perpendicular to each other?     (i) x - y + 4 = 0 , x + y - 6 = 0                         (ii) x + 2y - 6 = 0 ,   2x-y + 8 =0

Answer:

i)

To draw the line x - y + 4 = 0

x 0 -4
y 4 0

To draw the line x + y - 6 = 0

x 0 6
y 6 0

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Intersection is (1, 5) . They are perpendicular (from the graph we can see that). Also the slope of the first line is 1 while the slope of the second line is -1 . We know if the product of the two slopes is -1 (which is the case here) the lines are perpendicular.

ii)

To draw the line x + 2y - 6 = 0

x 0 6
y 3 0

To draw the line 2x-y + 8 =0

x 0 4
y 8 0

2019-03-10_10-22-07

Intersection is (-2, 4) . They are perpendicular (from the graph we can see that). Also the slope of the first line is - (\frac{1}{2}) while the slope of the second line is 2 . We know if the product of the two slopes is -1 (which is the case here) the lines are perpendicular.

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Question 6: Draw the graph of the following pairs of lines on the same graph paper and hence check whether they are parallel or not:

(i) y=3x+2 ,   y=3x-4     (ii) 2x+y-5=0 ,    x-2y +7 =0                           (iii) 3x+2y- 8 = 0 ,    3x+2y +12= 0

Answer:

(i) y=3x+2 ,   y=3x-4

To draw the line y=3x+2

x 0 -(2/3)
y 2 0

To draw the line y=3x-4

x 0 (4/3)
y -4 0

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The lines on the graph are parallel. Slope of first line is 3 while the slow of the second line is also 3 . This also proves that the lines are parallel as the slopes of the lines are equal.

(ii) 2x+y-5=0 ,    x-2y +7 =0

To draw the line 2x+y-5=0

x 0 2.5
y 5 0

To draw the line x-2y +7 =0

x 0 -7
y 3.5 0

2019-03-10_10-53-24

The lines on the graph are not parallel. Slope of first line is -2 while the slow of the second line is also -\frac{1}{2} . This also proves that the lines are parallel as the slopes of the lines are not equal.

(iii) 3x+2y- 8 = 0 ,    3x+2y +72= 0

To draw the line 3x+2y- 8 = 0

x 0 (8/3)
y 4 0

To draw the line 3x+2y +12= 0

x 0 -4
y -6 0

2019-03-10_11-03-53

The lines on the graph are parallel. Slope of first line is -(3/2) while the slow of the second line is also -(3/2) . This also proves that the lines are parallel as the slopes of the lines are equal.

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