Step 1 :The equation of the line is given by \(-x+4y=8\).
Step 2 :First, we find the x-intercept by setting y = 0 in the equation. This gives us \(-x+4(0)=8\), which simplifies to \(-x=8\). Solving for x, we get \(x=-8\).
Step 3 :Next, we find the y-intercept by setting x = 0 in the equation. This gives us \(-0+4y=8\), which simplifies to \(4y=8\). Solving for y, we get \(y=2\).
Step 4 :Thus, the x-intercept of the line is \(-8\) and the y-intercept is \(2\).
Step 5 :We can now plot the line using these intercepts. The line crosses the x-axis at \(-8\) and the y-axis at \(2\).
Step 6 :\(\boxed{\text{The x-intercept of the line is -8 and the y-intercept is 2.}}\)