1. The problem asks for the x-intercept of the line given by the equation $$4x - 5y = 2$$ in the xy-plane. The x-intercept is the point where the graph crosses the x-axis, so the y-coordinate is 0. 2. To find the x-intercept, substitute $$y = 0$$ into the equation: $$4x - 5(0) = 2$$ which simplifies to $$4x = 2$$ 3. Solve for $$x$$ by dividing both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{2}{\cancel{4}}$$ which simplifies to $$x = \frac{2}{4}$$ 4. Simplify the fraction: $$x = \frac{1}{2}$$ 5. Therefore, the x-intercept is at the point $$\left(\frac{1}{2}, 0\right)$$ and the value of $$x$$ is $$\frac{1}{2}$$.