Help with linear equations

In summary, the conversation discusses how to graph the equations y=x-2 and y=4-x and find the coordinates of the point of intersection. The process involves solving for x when both equations are equal, plotting the points (x,y) and drawing a line through them, and finding the intersecting point. It is also suggested to use the equations given and do the arithmetic to find the value of y.
  • #1
caprija
34
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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?
 
  • #6
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?
 

1. What are linear equations?

Linear equations are mathematical expressions that involve two variables and can be represented by a straight line on a graph. They are commonly used to model real-world relationships and can be solved to find the values of the variables.

2. How do I solve a linear equation?

To solve a linear equation, you can use the basic algebraic principles of adding, subtracting, multiplying, and dividing to isolate the variable on one side of the equation. The goal is to end up with the variable equal to a specific number, which represents its value.

3. What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept, or the point where the line crosses the y-axis. This form is useful for graphing and solving linear equations.

4. Can linear equations have more than two variables?

No, linear equations can only have two variables. This is because they are represented by a straight line on a graph, which only has two dimensions. If there are more than two variables, it is considered a system of linear equations.

5. How can I use linear equations in real life?

Linear equations are commonly used in real life to model relationships between two variables, such as distance and time, cost and quantity, or temperature and time. They can also be used to make predictions and solve problems in fields such as economics, engineering, and physics.

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