Question

1. graph the line that has a slope of \\(\frac{1}{6}\\) and includes the point \\((0, 0)\\).
2. click to select points on the graph.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the line passes through the point $(0,0)$ and has a slope $m=\frac{1}{6}$.
Substitute $x = 0$, $y = 0$ and $m=\frac{1}{6}$ into the equation $y=mx + b$:
$0=\frac{1}{6}(0)+b$
So, $b = 0$. The equation of the line is $y=\frac{1}{6}x$.

Step2: Find two points on the line

We already know that the line passes through $(0,0)$ (the origin). To find another point, we can use the slope. The slope $m=\frac{1}{6}=\frac{\text{rise}}{\text{run}}$. This means that for a run (change in $x$) of 6 units, the rise (change in $y$) is 1 unit.
Starting from the point $(0,0)$, if we move 6 units to the right (increase $x$ by 6, so $x=0 + 6=6$) and 1 unit up (increase $y$ by 1, so $y = 0+1 = 1$), we get the point $(6,1)$.

To graph the line, we plot the points $(0,0)$ and $(6,1)$ (and other points can be found using the slope, such as $(12,2)$ etc.) and then draw a straight line through them.

Answer:

To graph the line with slope $\frac{1}{6}$ passing through $(0,0)$:

1. Plot the point $(0,0)$ (the origin) on the coordinate plane.
2. Use the slope $\frac{1}{6}$: from $(0,0)$, move 6 units to the right (along the x - axis) and 1 unit up (along the y - axis) to plot the point $(6,1)$.
3. Draw a straight line passing through the points $(0,0)$ and $(6,1)$ (and extend it in both directions).