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Question: How do you find the x and y intercept of \[3x - 3y = 9\]?...

How do you find the x and y intercept of 3x3y=93x - 3y = 9?

Explanation

Solution

x-intercept can be found by substituting the value of ‘y’ is equal to zero in the given equation. Similarly we can find the y-intercept by substituting the value of ‘x’ equal to zero in the given equation. In other words ‘x’ intercept is defined as a line or a curve that crosses the x-axis of a graph and ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph.

Complete step-by-step solution:
Given, 3x3y=93x - 3y = 9.
To find the ‘x’ intercept put y=0y = 0 in the above equation,
3x3(0)=9\Rightarrow 3x - 3(0) = 9
3x=9\Rightarrow 3x = 9
Divide by 3 on both sides of the equation,
x=93\Rightarrow x = \dfrac{9}{3}
x=3\Rightarrow x = 3.
Thus ‘x’ intercept is 3.
To find the ‘y’ intercept put x=0x = 0 in the above equation,
3(0)3y=9\Rightarrow 3(0) - 3y = 9
3y=9\Rightarrow - 3y = 9
Divide by 3 - 3 on both sides of the equation,
y=93\Rightarrow y = - \dfrac{9}{3}
y=3\Rightarrow y = - 3.
Thus ‘y’ intercept is -3.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 3 and y-axis at -3.

Note: We can solve this using the standard intercept form. That is the equation of line which cuts off intercepts ‘a’ and ‘b’ respectively from ‘x’ and ‘y’ axis is xa+yb=1\dfrac{x}{a} + \dfrac{y}{b} = 1. We convert the given equation into this form and compare it will have a desired result.
Given 3x3y=93x - 3y = 9
Now we need 1 on the right hand side of the equation, so divide the whole equation by 9. We have,
3x3y9=99\dfrac{{3x - 3y}}{9} = \dfrac{9}{9}
Splitting the terms we have,
3x93y9=99\dfrac{{3x}}{9} - \dfrac{{3y}}{9} = \dfrac{9}{9}
x3y3=1\Rightarrow \dfrac{x}{3} - \dfrac{y}{3} = 1
That is we have,
x3+y3=1\Rightarrow \dfrac{x}{3} + \dfrac{y}{{ - 3}} = 1. On comparing with standard intercept form we have ‘x’ intercept is 3 and y intercept is -3. In both the cases we have the same answer.