Question

will mark brainliest for answer !! the answer choices to the drop down menu are equal to, greater than, or less than

Answer 1

.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:

$y=x-6$

This equation is written in slope-intercept form:

$y=mx+b$

Where m is the slope of the line and b represents the y-intercept.

Therefore in our equation:

$y=x-6$

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.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{10+5}{5-0}= \frac{15}{5} =3$

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.