Question

Read each situation carefully and then complete the table and graph then describe the slope of the line using complete sentences :A winter storm produces snow at a rate of 3 inches per hour. The equation y=3x represents the amount of snow accumulating per hour.1) Use a table to find the points to graph for the equation .2) Graph the equation .3) Describe in detail the slope of the line in detail :

Answer 1

The equation of a line that passes through the Origin has this form:

`y=mx`

Where "m" is the slope of the line.

For this case, the equation that represents the amount of snow accumulating per hour, is:

`y=3x`

1) So, in order to complete the table, you need to substitute into the equation each x-value given in the table and evaluate, in order to find the corresponding y-value. Then:

- For

`x=0`

You get:

`y=3(0)=0`

- For

`x=1`

You get:

`y=3(1)=3`

- For

`x=2`

You have that:

`y=3(2)=6`

- For

`x=3`

You have:

`y=3(3)=9`

- And for

`x=4`

You get:

`y=3(4)=12`

2) So, you have these points:

`\mleft(0,0\mright);\mleft(1,3\mright);\mleft(2,6\mright);\mleft(3,9\mright);\mleft(4,12\mright)`

Now you must plot them. The line must pass through these points.

3) You can identify that the slope of the given equation is:

`m=3`

Then, it is a positive slope, which means that the line rises moving from left to right. In this case, the slope indicates that the amount of snow that accumulates (its height) due the winter storm is: 3 inches per hour.

Therefore, the answers are:

1) Table:

2) Graph:

3) The slope of the line is 3. It is a positive slope that rises moving from left to right. It indicates that the height of the snow ccumulating per hour is 3 inches.