Mathematics
Grade-8
Easy
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.
