Question

# Identify the equation that represents the line containing points M and N?

- y = –4x – 3
- y = 4x – 3

Hint:

### 1. An equation refers to the relationship between 2 expressions represented with an equal to sign i.e. '='.

2. A point is said to be on a given line when the coordinates of that point when substituted in the given equation, satisfies the given equation.

## The correct answer is:

### GIVEN-

The given line passes through the points M & N as shown in the given graph.

TO FIND-

Equation of the given line.

SOLUTION-

From the given graph, we observe that-

M (0,-3) & N (8,-5)

We know that when a line passes through a given point, the coordinates of that point satisfies the equation of the said line.

Hence, we substitute the coordiantes of M & N in the given options to find the correct equation, for which LHS = RHS.

a. y = 4x - 3

We substitute M (0,-3) in the given equation-

y = 4x - 3

∴ -3 = 4(0) - 3

∴ -3 = 0 - 3

∴ -3 = -3

∴ LHS = RHS

We substitute N (8,-5) in the given equation-

y = 4x - 3

∴ -5 = 4(8) - 3

∴ -5 = 32 - 3

∴ -5 ≠ 29

∴ LHS ≠ RHS

Since, N (8,-5) does not satisfy the given equation, y = 4x - 3 is not the equation of the given line.

b. y = 1/4 x - 3

We substitute M (0,-3) in the given equation-

y = 1/4 x - 3

∴ -3 = 1/4 (0) - 3

∴ -3 = 0 - 3

∴ -3 = -3

∴ LHS = RHS

We substitute N (8,-5) in the given equation-

y = 1/4 x - 3

∴ -5 = 1/4 (8) - 3

∴ -5 = 2 - 3

∴ -5 ≠ -1

∴ LHS ≠ RHS

Since, N (8,-5) does not satisfy the given equation, y = 1/4 x - 3 is not the equation of the given line.

c. y = - 1/4 x - 3

We substitute M (0,-3) in the given equation-

y = -1/4 x - 3

∴ -3 = -1/4 (0) - 3

∴ -3 = 0 - 3

∴ -3 = -3

∴ LHS = RHS

We substitute N (8,-5) in the given equation-

y = 1/4 x - 3

∴ -5 = -1/4 (8) - 3

∴ -5 = -2 - 3

∴ -5 = -5

∴ LHS = RHS

Since both M (0,-3) and N (8,-5) satisfy the given equation, y = -1/4 x - 3 is the equation of the given line.

Final Answer:-

Option 'c' i.e. 'y = -1/4 x - 3' is the correct answer to the given question.

**Alternatively, we can use the 2 point formula to find the equation of the given line-****When we have 2 points that lie on a given line then we can find the equation of the said line by using the 2-point formula-**** (y-y1) = (y2-y1) * (x-x1)**** (x2-x1)****In the given question, x1 = 0, y1 = -3, x2 = 8 & y2 = -5****∴ (y-y1) = (y2-y1) * (x-x1)**** (x2-x1)****∴ [y- (-3)] = [-5 - (-3)] * (x - 0)**** (8-0)****∴ (y + 3) = (-5 + 3) * x**** 8****∴ 8 * (y + 3) = (-5 + 3) * x ................................... (Multiplying both sides by 8)****∴ 8y + 24 = -2x****∴ 8y = -2x - 24 ....................................... (Isolating y in LHS)****∴ y = -2/8 x - 24/8 .................................... (Dividing both sides by 8)****∴ y = -1/4 x - 3****Final Answer remains the same.**