Sketch the graph of graph y=(1/4)x -2, labelling the x-and y - intercept and the equation of the asymptote?

To sketch the graph of y=(1/4)x -2, we first need to find the x- and y-intercepts.

To find the x-intercept, we set y=0 and solve for x:
0 = (1/4)x - 2
1/4x = 2
x = 8

So the x-intercept is at (8,0).

To find the y-intercept, we set x=0 and solve for y:
y = (1/4)(0) - 2
y = -2

So the y-intercept is at (0,-2).

Next, we can find the equation of the asymptote. Since the equation is in the form y=mx+b, where m is the slope and b is the y-intercept, the asymptote is the line y=-2.

Now we can sketch the graph of y=(1/4)x -2, passing through the x-intercept (8,0) and the y-intercept (0,-2), with the asymptote y=-2.

Graph of y = (1/4)x - 2

Intercepts:

- x-intercept: To find the x-intercept, set y = 0 and solve for x:
```
0 = (1/4)x - 2
(1/4)x = 2
x = 8
```
Therefore, the x-intercept is (8, 0).
- y-intercept: To find the y-intercept, set x = 0 and solve for y:
```
y = (1/4)(0) - 2
y = -2
```
Therefore, the y-intercept is (0, -2).

Asymptote:

The asymptote of the graph is the line parallel to the x-axis that the graph approaches but never touches. In this case, the asymptote is the x-axis (y = 0).

Sketch:

1. Plot the x- and y-intercepts.
2. Draw a line passing through the intercepts.
3. Draw the asymptote as a horizontal line at y = 0.

The resulting graph looks like this:

[Image of the graph of y=(1/4)x - 2 with x- and y-intercepts and asymptote labeled]