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Maths-

General

Easy

Question

Which of the following could be an equation for the graph shown in the xy plave above?

y = - ( $\frac{2}{3}$ ) x + 8
y = - ( $\frac{3}{2}$ ) x + 4
y = - ( $\frac{1}{3}$ ) x + 4
y = - ( $\frac{4}{3}$ ) x + 8

The correct answer is: y = - ( $1 third$ ) x + 4

Hint:-
Reading the given graph, we observe that each point on x-axis represents 2 units and that on y=axis represents 1 unit.
2 point form of a line -
y - y¹ = [(y²- y¹) / (x² - x¹)] * (x - x¹)
Step-by-step solution:-
The given line passes through the points A (12,0) & B (0,4)
∴ x1 = 1², y¹ = 0, x² = 0, y² = 4
Substituting these coordinates in 2 point form of a line, we get-
y - y¹ = [(y²- y¹) / (x² - x¹)] * (x - x¹)
∴ y - 0 = [(4 - 0) / (0 - 12)] * (x - 12)
∴ y = ( $negative 4 over 12$ ) * (x - 12)
∴ y = - $1 third$ * (x - 12)
∴ y = - $1 third$ x - (- $1 third$ ) 12
∴ y = - $1 third$ x - (-4)
∴ y = - $1 third$ x + 4
Final Answer:-
Option C i.e. y = - $1 third$ x + 4 is the correct Option.

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