To graph the equation ( y = \fracThe{ equation given is:

1[ y}{ = \frac{1}{33}x} +x 2 ) using + the slope and the2 y-intercept :

### Step]

-by-StepThis Explanation is:

1. Identify in the y-inter the slope-interceptcept: form ( y = mx + b \ -), where The: equation- $m is in$ slope is-inter the slope,

• $b$cept is form the ( y-inter ycept =.

From mx this + equation b: - The slope), ( where m = \ (frac m{ \1}{)3} \ is the), which means for every slope3 units you move horizontally and (along the x-axis), ( the graph moves up b1 unit vertically (along the y-axis). )- The y-inter iscept $b the = 2$, which is the point where y the graph-inter crossescept the. y -axis. So the graph - crosses the y-axis at ( ( Here0,, ( b2) \ =).

Steps2 to graph:

\1),. ** soPlot the the y-intercept graph crosses** the: Start ** by plottingy the-axis point at $( (0,0 ,2)$ on the2 y)**-axis.

. 22. Plot. Use the the slope y: From (-inter (0cept, 2): \ ), - move up 1 unit and Start right by 3 plotting units the to find the point next point. This gives the ( point0 \(, 2 ()3 on the graph,.

3. Use the3 slope) \ to). 3 plot. ** additionalDraw points the line:**: Connect - The these slope points with ( a straight m line, extending it in = \ bothfrac{1 directions.

}{3This} \ line) means "rise over run represents": the - Rise = 1 (move up 1 unit) - Run = 3 ( equationmove ( right y = \frac{31}{ units3) } x - + Starting from2 the \ y).

-interWouldcept you ( like ( me to help with additional questions or graphing0 tips?

Additional related questions:

1. What does the slope $\frac{,1}{3}$ mean geometrically?
2. How do you identify the slope and y-intercept from2 a graph)?
3. What is the \ significance of the), y-intercept in real-world move problems? up4 .1 How unit would and the graph change if the3 slope were units negative to?
4. How do you graph the the equation if it's in right standard form?

.Tip This gives: the The point slope ( ( ( m3 ,) gives3 the rate of change between x and y. A positive) slope \ means the graph rises).

as4 it. moves Plot the second to the point right.:

• Mark the point $(3, 3)$ on the graph.

5. Draw the line:
   • Use a ruler or straight edge to connect the two points $(0, 2)$ and $(3, 3)$. Extend the line in both directions.

Final Graph:

• The line will have a gentle upward slope since $\frac{1}{3}$ is positive but less steep.
• The line crosses the y-axis at $(0, 2)$.

Would you like me to show this graph visually or explain further? Let me know!

Related Questions:

1. How do you determine the slope from two points on a line?
2. What happens to the graph if the slope is negative?
3. How do you write an equation if you are given the slope and one point?
4. How does changing the y-intercept affect the graph of the line?
5. What is the slope-intercept form, and why is it useful?

Tip: Always remember, the slope tells you the steepness and direction of a line, and the y-intercept tells you where the line crosses the y-axis.