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Question
Which of the following graphs correctly represents the equation 3x + 4 = x− 4?
Which of the following graphs correctly represents the equation 3x + 4 = x− 4?
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Solution
The correct option is C
The given equation is 3x + 4 = x − 4.
This equation can be solved as
3x + 4 = x − 4
3x − x = − 4 − 4
2x = −8
x = −4
Now, the equation 3x + 4 = x − 4 reduces to x = −4.
x = −4 can be written asx + 0 × y = −4 which is a linear equation in the variables x and y.
Then, for any value of y, the value of x will be −4 only.
Therefore, the line representing equation 3x + 4 = x − 4 is the line at a distance of 4 units to the left of y-axis and parallel to it.
This can be shown as
Thus, the graph shown in alternative C correctly represents the given equation.
The given equation is 3x + 4 = x − 4.
This equation can be solved as
3x + 4 = x − 4
3x − x = − 4 − 4
2x = −8
x = −4
Now, the equation 3x + 4 = x − 4 reduces to x = −4.
x = −4 can be written asx + 0 × y = −4 which is a linear equation in the variables x and y.
Then, for any value of y, the value of x will be −4 only.
Therefore, the line representing equation 3x + 4 = x − 4 is the line at a distance of 4 units to the left of y-axis and parallel to it.
This can be shown as
Thus, the graph shown in alternative C correctly represents the given equation.