Question

How do you find the x and y intercepts of \[4x - 9y = 6\]?

Answer 1

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,
\[\Rightarrow 4x - 9y = 6\].
To find the x-intercept we substitute \[y = 0\] in the given equation we have,
\[\Rightarrow 4x - 9\left( 0 \right) = 6\]
\[\Rightarrow 4x = 6\]
Dividing by 4 on both side of the equation we have
\[\Rightarrow x = \dfrac{6}{4}\]
\[\Rightarrow x = \dfrac{3}{2}\]
\[ \Rightarrow x = 1.5\]
That is x-intercept is 1.5
To find the y-intercept we substitute \[x = 0\] in the given equation we have,
\[\Rightarrow 4(0) - 9y = 6\]
\[\Rightarrow - 9y = 6\]
Divide the whole equation by -9
\[\Rightarrow y = \dfrac{6}{{ - 9}}\]
\[\Rightarrow y = \dfrac{2}{{ - 3}}\]
\[ \Rightarrow y = - 0.666\]
Rounding off we have,
\[ \Rightarrow y = - 0.67\]
That is y-intercept is 6.

Thus, we have the x-intercept is 1.5. The y-intercept is -0.67.

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,
\[4x - 9y = 6\]
We need 1 on the right hand side of the equation. So we divide the equation by 6 on both sides.
\[\dfrac{{4x - 9y}}{6} = \dfrac{6}{6}\]
Separating the terms in the left hand side of the equation. We have,
\[\dfrac{{4x}}{6} + \dfrac{{ - 9y}}{6} = \dfrac{6}{6}\]
Now cancelling we have,
\[\dfrac{x}{{1.5}} + \dfrac{y}{{ - 0.67}} = 1\].
Now comparing with the standard intercept equation we have,
The x-intercept is 1.5. The y-intercept is -0.67. In both the methods we have the same answer. We can choose any one method to solve this.