How to Graph Linear Equations and Determine Their Intersection Point?

  • Context: High School 
  • Thread starter Thread starter caprija
  • Start date Start date
  • Tags Tags
    Linear Linear equations
Click For Summary

Discussion Overview

The discussion revolves around the methods for graphing the linear equations y=x-2 and y=4-x, as well as determining their intersection point. It includes both graphical and algebraic approaches to solving the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant requests an explanation for graphing the equations and finding their intersection point.
  • Another participant suggests equating the two expressions for y to solve for x, implying that the y-values must be the same at the intersection.
  • Several participants propose specific values for x (0 and 2) to calculate corresponding y-values for the first equation, y=x-2, and suggest plotting these points to form the line.
  • Similar calculations and plotting are suggested for the second equation, y=4-x, to visualize the lines and find their intersection.
  • There is a repeated inquiry about using the slope-intercept form (y=mx+b) and how to determine the value of y from the given equations.
  • One participant emphasizes the importance of finding the intersection points of the axes to aid in graphing the lines.
  • Another participant questions whether the previous suggestions were understood and encourages the use of the given equations for finding y.

Areas of Agreement / Disagreement

Participants express various methods for graphing and finding the intersection, but there is no consensus on a single approach or resolution to the problem. Multiple viewpoints on how to proceed remain evident.

Contextual Notes

Some participants mention specific points to plot, but there is no agreement on the final coordinates of the intersection point or the completeness of the algebraic method suggested.

Who May Find This Useful

This discussion may be useful for students learning to graph linear equations and find intersection points, as well as those seeking different approaches to solving similar mathematical problems.

caprija
Messages
34
Reaction score
0
Could someone please explain how to graph y=x-2 and y=4-x
and find the coordinates of the point of intersection.
 
Mathematics news on Phys.org
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?
 

Similar threads

  • · Replies 18 ·
Replies
18
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 19 ·
Replies
19
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K