**Practice Problems of Finding Equation of the Line :**

Here we are going to see, some example problems to show finding equation of the line with the given details.

**Question 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

**Question 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

**Question 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

After having gone through the stuff given above, we hope that the students would have understood, "Practice Problems of Finding Equation of the Line".

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