Graph a line that contains the point $(-6,1)$ and has a slope of 5 .

Step 1 ：Given a point $(-6,1)$ and a slope of 5, we want to find the equation of the line that passes through this point and has this slope.

Step 2 ：The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 3 ：We know the slope $m$ is 5, and we know that the line passes through the point $(-6,1)$. We can substitute these values into the equation to solve for $b$.

Step 4 ：Substituting $m = 5$, $x = -6$, and $y = 1$ into the equation, we get $1 = 5(-6) + b$. Solving for $b$, we find $b = 31$.

Step 5 ：Now that we have the slope and the y-intercept, we can write the equation of the line as $y = 5x + 31$.

Step 6 ：\(\boxed{y = 5x + 31}\) is the final answer.