Answer:
We conclude that option 'C' i.e. 1/3x+1=2x-4 is the correct option.
Step-by-step explanation:
From the given graph, it is clear that the two lines meet at the point (3, 2).
In other words,
Thus,
The point of intersection between two lines is:
(x, y) = (3, 2)
Here:
x = 3 is the value of the x-coordinate
y = 2 is the value of the y-coordinate
Now, checking the equation i.e. 1/3x+1=2x-4 to determine whether the equation contains the correct value of x-coordinate or not.
[tex]\frac{1}{3}x+1=2x-4[/tex]
Subtract 1 from both sides
[tex]\frac{1}{3}x+1-1=2x-4-1[/tex]
Simplify
[tex]\frac{1}{3}x=2x-5[/tex]
subtract 2x from both sides
[tex]\frac{1}{3}x-2x=2x-5-2x[/tex]
Simplify
[tex]-\frac{5}{3}x=-5[/tex]
Multiply both sides by 5
[tex]3\left(-\frac{5}{3}x\right)=3\left(-5\right)[/tex]
Simplify
[tex]-5x=-15[/tex]
Divide both sides by -5
[tex]\frac{-5x}{-5}=\frac{-15}{-5}[/tex]
Simplify
[tex]x=3[/tex]
Therefore, the value of x = 3
Conclusion:
We conclude that option 'C' i.e. 1/3x+1=2x-4 is the correct option.
