Answer: The required x-intercept is (3.6, 0) and y-intercept is (0, -1.2).
Step-by-step explanation: We are given to find the x-intercept and y-intercept of the line described by the following equation :
\(3x-9y=10.8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that
x-intercept is a point on the line where the line crosses the x-axis and y-intercept is a point where line crosses the y-axis.
On x-axis, y = 0 and on y-axis, x = 0.
If y = 0, then from equation (i), we get
\(3x-0=10.8\\\\\Rightarrow 3x=10.8\\\\\Rightarrow x=\dfrac{10.8}{3}\\\\\Rightarrow x=3.6.\)
And, if x = 0, then from equation (i), we get
\(0-9y=10.8\\\\\Rightarrow 9y=-10.8\\\\\Rightarrow y=-\dfrac{10.8}{9}\\\\\Rightarrow y=-1.2.\)
Thus, the required x-intercept is (3.6, 0) and y-intercept is (0, -1.2).
