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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.

answer: 20

step-by-step explanation: