1. The problem is to analyze the linear equation $y = 5x$. 2. This is a linear function where $y$ depends on $x$ with a slope of 5 and a y-intercept of 0. 3. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 4. Here, $m = 5$ and $b = 0$, so the line passes through the origin and rises 5 units vertically for every 1 unit horizontally. 5. To find the x-intercept, set $y=0$: $$0 = 5x \implies x = 0$$ 6. To find the y-intercept, set $x=0$: $$y = 5 \times 0 = 0$$ 7. Therefore, the line passes through the origin (0,0). 8. The function is increasing because the slope is positive. Final answer: The line $y=5x$ has slope 5, passes through the origin, and has intercepts at (0,0).