The given equation is:

$y = \dfrac{6}{5}x + 1$

This is the equation of a straight line in slope-intercept form, where:

• The slope $m = \dfrac{6}{5}$
• The y-intercept $b = 1$

To graph this line:

1. Start by plotting the y-intercept: This is where the line crosses the y-axis. In this case, the y-intercept is $b = 1$. So, plot the point $(0, 1)$.

2. Use the slope to find another point: The slope $\dfrac{6}{5}$ means that for every 5 units you move horizontally to the right (positive x-direction), you move 6 units vertically up (positive y-direction).

   • From the point $(0, 1)$, move 5 units to the right (to $x = 5$), and 6 units up. This brings you to the point $(5, 7)$.

3. Draw the line: Once you have two points, $(0, 1)$ and $(5, 7)$, you can draw a straight line through them. This line is the graph of the equation $y = \dfrac{6}{5}x + 1$.

Would you like more details on how to graph lines or help with similar equations?

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Here are some follow-up questions you may find interesting:

1. How do you graph a line when the slope is negative?
2. What are some real-life examples where a line like $y = \dfrac{6}{5}x + 1$ might appear?
3. How can you find the equation of a line if you're given two points?
4. How do you graph a line with a slope of zero?
5. What happens to the graph of a line when the y-intercept is changed?

Tip: To graph lines quickly, always identify the slope and y-intercept, as they are key to plotting points efficiently.