The slope of the line is $5$, and the y-intercept is $1$.

In the equation of a straight line, given by $y = mx + c$, the variable $m$ denotes the slope (or gradient), while $c$ signifies the y-intercept. The slope indicates the steepness of the line, whereas the y-intercept represents the point where the line intersects the y-axis. For the specific equation $y = 5x + 1$, the slope $m$ is $5$. This implies that for every unit increase in $x$, the value of $y$ increases by $5$ units, resulting in a relatively steep line.

The y-intercept $c$ is $1$, which indicates that the line crosses the y-axis at the point $(0, 1)$. This point represents the value of $y$ when $x$ is $0$. Understanding these components is essential for quickly sketching the graph of the line and analyzing its behavior. For example, knowing that the slope is positive suggests that the line ascends as it moves from left to right.

In summary, the slope and y-intercept are critical characteristics of a linear equation that facilitate the understanding and graphing of the line. A slope of $5$ indicates a steep incline, while a y-intercept of $1$ shows the point at which the line meets the y-axis.