What is the slope, m, of the graph of this line? What is the y-intercept of the graph of this line? Graph the linear equation.

Steps to Solve

1. Identify the slope from the equation The equation is given as $y = \frac{1}{5}x + 3$. The slope $m$ is the coefficient of $x$, which is $\frac{1}{5}$.

2. Determine the y-intercept of the graph The y-intercept is the constant term in the equation, which is where the line crosses the y-axis. In this case, it is $3$. We can express the y-intercept as the ordered pair $(0, 3)$.

3. Summarize the slope and y-intercept We have found that the slope $m = \frac{1}{5}$ and the y-intercept is $(0, 3)$.

4. Graph the linear equation To graph the equation, plot the y-intercept $(0, 3)$ on the coordinate plane. From there, use the slope $\frac{1}{5}$ to find another point. This means that for every $5$ units you move to the right (along the x-axis), you will move up $1$ unit (along the y-axis).

   • Starting from $(0, 3)$, moving right $5$ units to $(5, 3)$ and then up $1$ unit gives us the point $(5, 4)$.
   • Draw a straight line through the points $(0, 3)$ and $(5, 4)$ to complete the graph.