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How do you find the intercepts of \[2x + y = 6\]?

seo-qna
Last updated date: 20th Jun 2024
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Answer
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Hint: Here we need to find x-intercept and y-intercept. We know that x-intercept is a point on the graph where ‘y’ is zero.
Also we know that y-intercept is a point on the graph where ‘x’ is zero. In other words the value of ‘x’ at ‘y’ is equal to zero is called x-intercept. The value of ‘y’ at ‘x’ is equal to zero is called t-intercept. Using this definition we can solve the given problem.

Complete step by step solution:
Given,
\[2x + y = 6\].
To find the x-intercept we substitute \[y = 0\] in the given equation we have,
\[2x + (0) = 6\]
\[2x = 6\]
Dividing by 2 on both side of the equation we have
\[x = \dfrac{6}{2}\]
\[x = 3\]
That is x-intercept is 3.
To find the y-intercept we substitute \[x = 0\] in the given equation we have,
\[2(0) + y = 6\]
\[y = 6\]
That is y-intercept is 6.
Thus, we have the x-intercept is 3. The y-intercept is 6.

Note: We can also solve this by converting the given equation into the equation of straight line intercept form. That is \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]. Where ‘a’ is a x-intercept and ‘b’ is called y-intercept.
Now given,
\[2x + y = 6\]
We need 1 on the right hand side of the equation. So we divide the equation by 6 on both sides.
\[\dfrac{{2x + y}}{6} = \dfrac{6}{6}\]
Separating the terms in the left hand side of the equation. We have,
\[\dfrac{{2x}}{6} + \dfrac{y}{6} = \dfrac{6}{6}\]
Now cancelling we have,
\[\dfrac{x}{3} + \dfrac{y}{6} = 1\].
Now comparing with the standard intercept equation we have,
The x-intercept is 4. The y-intercept is 3. In both the methods we have the same answer. We can choose any one method to solve this.