Answer:
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.
