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compare the linear functions expressed by the equation, y = –x + 3, and by data in the table.

explain how to determine if these two are the same function expressed in different ways

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

need points to ask question

step-by-step explanation:

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.