.Answer:
The rate of change for y=x+6 is less than the slope of the line represented by the table.
Step-by-step explanation:
First let's look at our equation:
[tex]y=x-6[/tex]
This equation is written in slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope of the line and b represents the y-intercept.
Therefore in our equation:
[tex]y=x-6[/tex]
Our slope is 1 (invisible 1 in front of x since 1 times x is x) and it also has a y-intercept of -6.
Next let's look at our table and choose any two points. In this case I choose (0,-5) and (5,10). It doesn't matter which two you decide to choose. Now, let's calculate the slope of this line by using the following equation.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{10+5}{5-0}= \frac{15}{5} =3[/tex]
and so the line that the table represents is more than to y=x-6. Furthermore, the equation for the table is y=3x-5, this is because (0,-5) is the y-intercept for this line.
