Let's analyze the equation of the line provided:

$y - 5 = \frac{1}{5}(x - 1)$

This equation is in point-slope form, which is:

$y - y_1 = m(x - x_1),$

where $m$ is the slope, and $(x_1, y_1)$ is a point on the line. From the equation:

• The slope ($m$) is $\frac{1}{5}$,
• The point $(x_1, y_1)$ is $(1, 5)$.

Steps to Graph the Line:

1. Plot the point $(1, 5)$ as given in the equation.

2. Use the slope $\frac{1}{5}$ (rise over run):

   • Rise = $1$ (move up by 1 unit),
   • Run = $5$ (move right by 5 units).

   Starting from $(1, 5)$, moving 5 units right and 1 unit up takes you to $(6, 6)$.

3. Plot this second point $(6, 6)$.

4. Draw a straight line through these two points.

Key Points to Plot:

• $(1, 5)$ — starting point.
• $(6, 6)$ — using the slope.

Would you like me to explain more details about graphing? Let me know!

Related Questions:

1. What is the slope-intercept form of this equation?
2. How do you convert from point-slope form to slope-intercept form?
3. What happens to the graph if the slope is negative?
4. How do you determine if two lines are parallel or perpendicular?
5. How do you find the x-intercept of this line?

Tip:

When graphing using slope, always move from one point using "rise over run" to plot additional points. This ensures accuracy!