How to Graph Linear Equations and Determine Their Intersection Point?

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To graph the equations y=x-2 and y=4-x, first determine the coordinates for specific x-values, such as x=0 and x=2. Plot these points for each equation to create straight lines. The intersection point can be found by setting the two equations equal to each other and solving for x. After finding the x-coordinate of the intersection, substitute it back into either equation to find the corresponding y-coordinate. This process allows for both graphical and algebraic determination of the intersection point.
caprija
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Could someone please explain how to graph y=x-2 and y=4-x
and find the coordinates of the point of intersection.
 
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If the coördinates are the same, then surely the y-values are.
Let both expressions for y in terms of x equal and solve for x.
 
y= x-2

If x= 0, what is y?

If x= 2, what is y?

can you plot those two (x,y) points?

Since the graph of y= x- 2 is a straight line just draw the line between those two points.

Now do exactly the same thing using y= 4- x
If x= 0, what is y?
If x= 2, what is y?

Plot those two (x,y) points and draw the line through them.

Where do those two line cross?
 
HallsofIvy said:
y= x-2

If x= 0, what is y?

If x= 2, what is y?

can you plot those two (x,y) points?

Since the graph of y= x- 2 is a straight line just draw the line between those two points.

Now do exactly the same thing using y= 4- x
If x= 0, what is y?
If x= 2, what is y?

Plot those two (x,y) points and draw the line through them.

Where do those two line cross?
do I use y=mx+b?

How would I find out what y equals?
 
Where you able to find the two points HallsofIvy asked you to?
He was guiding you to the interesection points of the axis, allowing you to graph the line.
Then, you can graphically find the coördinates of the point of intersection.

If you need to find it algebraically, did you understand my suggestion?
 
caprija said:
do I use y=mx+b?

How would I find out what y equals?
You said you were given y=x-2 and y=4-x. Why not use them?

How do you find out what y equals? Do the arithemetic! What do you think "y= x- 2" means?
 

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