FINDING EQUATION OF LINE FROM GRAPH WORKSHEET

Find equation of the line from the following graph given :

Problem 1  :

Problem 2 :

Problem 3 :

Problem 4 :

Problem 5 :

Problem 6 :

1. Solution :

Slope of a line  =  1/3

y – intercept(b)  =  2

Equation of a straight line y  =  mx + b

y  =  1/3x + 2

3y  =  x + 6

x – 3y + 6  =  0

So, the required equation is x – 3y + 6  =  0.

2. Solution :

x – intercept form a  =  2

N – intercept form b  =  -1

By using x – intercept and y – intercept formula,

x/a + y/b  =  1

x/2 + N/(-1)  =  1

x/2 – N/1  =  1

- N  =  - 1/2x + 1

N  =  (1/2)x - 1

So, the required equation is N  =  (1/2)x - 1

3. Solution  :

s – intercept form a  =  4

G – intercept form b  =  2

By using x – intercept and y – intercept formula,

x/a + y/b  =  1

S/4 + G/2  =  1

G/2  =  - S/4 + 1

G  =  - S/2 + 2

G  =  (-1/2)S + 2

So, the required equation is G  =  (-1/2)S + 2

4. Solution :

In figure, the straight line passes through two points (4, -3) and (0, 2)

By using two points formula,

(y – y₁)/(y₂ – y₁)  =  (x – x₁)/(x₂ – x₁)

We have two points (4, -3) and (0, 2)

(4, -3)----->(x₁, y₁)

(0, 2)----->(x₂, y₂)

By applying the values, we get

(H+3)/(2+3)  =  (g–4)/(0–4)

(H+3)/5  =  (g–4)/(-4)

(-4) (H+3)  =  5 (g–4)

- 4H–12  =  5g–20

- 4H  =  5g–20+12

- 4H  =  5g–8

H  =  (-5/4)g + 2

So, the required equation is H  =  (-5/4)g + 2

5. Solution :

In figure, the straight line passes through two points (10, 2) and (0, 1)

By using two points formula,

(y – y₁)/(y₂ – y₁)  =  (x – x₁)/(x₂ – x₁)

We have two points (10, 2) and (0, 1)

(10, 2)------>(x₁, y₁)

(0, 1)------>(x₂, y₂)

By applying the values, we get

(F–2)/(1–2)  =  (x–10)/(0-10)

(F–2)/(-1)  =  (x–10)/(-10)

(-10) (F–2)  =  (-1) (x–10)

-10F+20  =  - x+10

- 10F  =  - x+10–20

- 10F  =  -x–10

F  =  (1/10)x + 1

So, the required equation is F  =  (1/10)x + 1

6. Solution :

In figure, the straight line passes through two points (6, -3) and (0, -2)

By using two points formula,

(y – y₁)/(y₂ – y₁)  =  (x – x₁)/(x₂ – x₁)

We have two points (6, -3) and (0, -2)

(6, -3)------>(x₁, y₁)

(0, -2)------>(x₂, y₂)

By applying the values, we get

(P+3)/(-2+3)  =  (t–6)/(0–6)

(P+3)/1  =  (t–6)/(-6)

(-6) (P+3)  =  t–6

- 6P–18  =  t–6

- 6P  =  t–6+18

- 6P  =  t+12

P  =  (-1/6)t - 2

So, the required equation is P  =  (-1/6)t – 2

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