Example 1 :
Find the equation of a straight line which has Slope -5/4 and passing through the point (–1, 2).
Solution :
Slope = -5/4
Equation of the line passing through the point (-1, 2)
y - y_{1} = m(x - x_{1})
(y - 2) = (-5/4) (x - (-1))
4(y - 2) = - 5(x + 1)
4y - 2 = -5x - 5
5x + 4y - 2 + 5 = 0
5x + 4y + 3 = 0
Example 2 :
You are downloading a song. The percent y (in decimal form) of mega bytes remaining to get downloaded in x seconds is given by y = −0.1x +1.
(i) graph the equation.
(ii) find the total MB of the song.
(iii) after how many seconds will 75% of the song gets downloaded?
(iv) after how many seconds the song will be downloaded completely?
Solution :
y = −0.1x +1
x |
-10 |
0 |
10 |
y |
2 |
1 |
2 |
Points to be plotted :
(-10, 2) (0, 1) (10, 2)
(ii) find the total MB of the song.
To find the total MB of the song, we have to assign the value of x as 0.(The initial point of downloading is at 0 seconds)
y = −0.1x +1
If x = 0
y = -0.1(0) + 1
y = 1
Hence the size of song to be downloaded is 1 MB.
(iii) after how many seconds will 75% of the song gets downloaded?
y = 75% = 0.75
y = −0.1x +1
0.75 = -0.1x + 1
0.75 - 1 = -0.1x
-0.25 = -0.1x
x = 0.25/(0.1)
x = 2.5 seconds
Hence after 2.5 seconds 75% of the song gets downloaded.
(iv) after how many seconds the song will be downloaded completely?
Now, the size of MB is 0
0 = -0.1 x + 1
0.1x = 1
x = 1/0.1 = 10
Hence it will take 10 seconds to download the song completely
Example 3 :
Find the equation of a line whose intercepts on the x and y axes are given below.
(i) 4, –6
Solution :
x intercept = a = 4
y intercept = b = -6
(x/a) + (y/b) = 1
(x/4) + (y/(-6)) = 1
(x/4) - (y/6) = 1
(6x - 4y)/24 = 1
6x - 4y = 24
3x - 2y = 12
(ii) -5, 3/4
x intercept = a = -5
y intercept = b = 3/4
(x/a) + (y/b) = 1
(x/(-5)) + (y/(3/4)) = 1
(-x/5) + (4y/3) = 1
(-3x + 20y)/15 = 1
-3x + 20y = 15
3x - 20y + 15 = 0
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