Question

graph the line that has a slope of \\(\frac{1}{8}\\) and includes the point (0, 8). 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 slope $m=\frac{1}{8}$ and the line passes through the point $(0,8)$. The y - intercept $b$ is the value of $y$ when $x = 0$, so $b = 8$.
So the equation of the line is $y=\frac{1}{8}x + 8$.

Step2: Identify two points on the line

We already have the y - intercept point $(0,8)$. To find another point, we can use the slope. The slope $m=\frac{\text{rise}}{\text{run}}=\frac{1}{8}$. This means that for a run (change in $x$) of 8 units, the rise (change in $y$) is 1 unit.
Starting from the point $(0,8)$, if we add 8 to the $x$ - coordinate (run = 8) and add 1 to the $y$ - coordinate (rise = 1), we get the point $(0 + 8,8+1)=(8,9)$.

Step3: Plot the points and draw the line

We plot the points $(0,8)$ and $(8,9)$ (and we could find more points using the slope if needed) and then draw a straight line through them.

To graph the line:

1. Locate the point $(0,8)$ on the coordinate plane (this is on the y - axis, 8 units up from the origin).
2. Locate the point $(8,9)$ (8 units to the right on the x - axis from the origin and 9 units up on the y - axis).
3. Use a straightedge to draw a line connecting these two points (and extending it in both directions).

Answer:

The line is graphed by plotting the points $(0,8)$ and $(8,9)$ (and other points found using the slope $\frac{1}{8}$) and drawing a straight line through them. The equation of the line is $y=\frac{1}{8}x + 8$.