Question
Question: How do you find the x and y intercept of \[3x - 3y = 9\]?...
How do you find the x and y intercept of 3x−3y=9?
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, 3x−3y=9.
To find the ‘x’ intercept put y=0 in the above equation,
⇒3x−3(0)=9
⇒3x=9
Divide by 3 on both sides of the equation,
⇒x=39
⇒x=3.
Thus ‘x’ intercept is 3.
To find the ‘y’ intercept put x=0 in the above equation,
⇒3(0)−3y=9
⇒−3y=9
Divide by −3 on both sides of the equation,
⇒y=−39
⇒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 ax+by=1. We convert the given equation into this form and compare it will have a desired result.
Given 3x−3y=9
Now we need 1 on the right hand side of the equation, so divide the whole equation by 9. We have,
93x−3y=99
Splitting the terms we have,
93x−93y=99
⇒3x−3y=1
That is we have,
⇒3x+−3y=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.