Question

# John is trying to find the equation of the line(s) represented by the following graph.

- 4x – 5y = 10
- 4x + 5y = 10
- Y = 4x + 2
- Y = 4x - 2

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: 4x – 5y = 10

### GIVEN-

The given line passes through the points (0,-2) & (2.5,0) as shown in the given graph.

TO FIND-

Equation of the given line.

SOLUTION-

From the given graph, we observe that-

(0,-2) & (2.5,0)

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 both the point s in the given options to find the correct equation, for which LHS = RHS.

a. 4x - 5y = 10

We substitute (0,-2) in the given equation-

4x - 5y = 10

∴ 4 (0) - 5 (-2) = 10

∴ 0 + 10 = 10

∴ 10 = 10

∴ LHS = RHS

We substitute (2.5,0) in the given equation-

4x - 5y = 10

∴ 4 (2.5) - 5 (0) = 10

∴ 10 - 0 = 10

∴ 10 = 10

∴ LHS = RHS

Since both (0,-2) and (2.5,0) satisfy the given equation, 4x - 5y = 10 is the equation of the given line.

Final Answer:-

Option 'a' i.e. '4x - 5y = 10' 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 = -2, x2 = 2.5 & y2 = 0****∴ (y-y1) = (y2-y1) * (x-x1)**** (x2-x1)****∴ [y- (-2)] = [0 - (-2)] * (x - 0)**** (2.5-0)****∴ (y + 2) = 2 * x**** 2.5****∴ 2.5 * (y + 2) = 2x ................................... (Multiplying both sides by 2.5)****∴ 2.5y + 5 = 2x****∴ 5 = 2x - 2.5y****∴ 10 = 4x - 5y****i.e. 4x - 5y = 10****Final Answer remains the same.**