graphing question

[MommyThrice]

Can this be solved without graphing?

 

y = -x+3

y = -2

[kiana]

Yes. Since y = -x + 3 AND y = -2, and they are the same y, -x + 3 = -2.

 

Another way to work it is if you subtract the first equation from the second, you get y-y = -2 - (-x + 3).

[CO MOM]

Yes, use substitution. Put -2 into the first equation for y and solve for x (end up with 5).

[creekland]

Absolutely. The solution is the point (5, -2) as it is the intersection of the two lines. While graphing will give it to you, so will algebra as mentioned by the previous poster. Since both "things" equal "y," set them equal to each other to solve for "x."

 

-2 = -x + 3

0 = -x + 5

x = 5

 

And since we know y = -2 (original info), then the solution is the point (5, -2).

[MommyThrice]

Yes. Since y = -x + 3 AND y = -2, and they are the same y, -x + 3 = -2.

 

Another way to work it is if you subtract the first equation from the second, you get y-y = -2 - (-x + 3).

 

How did you know the two y's were the same? What exactly does "y" stand for? I know m=slope, x=x-intercept, and b=y-intercept. What is y?

 

I THOUGHT I understood algebra!

[Guest Cheryl in SoCal]

How did you know the two y's were the same? What exactly does "y" stand for? I know m=slope, x=x-intercept, and b=y-intercept. What is y?

 

I THOUGHT I understood algebra!

x and y are the coordinates of a point

[Teachin'Mine]

When you draw the two lines in a cross - perpendicular to each other - the x is the horizontal line, and y is the vertical line. By solving that equation and coming up with the point (5, -2), it designates going right on the x axis to 5 and then going down two lines to negative 2. It would be in the lower right hand quadrant. But I'm not sure if this answered your question or not.

[MommyThrice]

So, y the y coordinate of ANY point on the line? And x is the x coordinate of that same point? But b is the where y actually intercepts the axis? NOW I know why b is called b, so it isn't confused with y.

 

Y'all are so helpful!!! :)

[MommyThrice]

...and if I had really thought about it, the two lines intercept where the two x's are equal and the two y's are equal.

[Nan in Mass]

A line with a formula like that is straight. The line is actually all the possible solutions to that formula. For example, if you graph all the possible solutions to x+y=3, x could be 1 and y could be two, or x could be 1/2 and y could be 2 1/2. If you plotted every single combination of x and y that was true for that formula, you would have a stright line. That is what the line IS. You have two formulas, each with a batch of x's and y's that make their formulas true. The intersection is the point (the x and the y) where BOTH formulas are true. You know that both y's are the same because that is the definition of intersection. When you "solve" two equations like this, you are looking for the intersection of their lines, which is the x and the y where both equations are true. In this case, one line is the set of all x and y combinations where x+y=3 (I rearranged the equation to make it look easy), and the other line is the set of all x and y combinations where y = -2 (which happens to be a horizontal straight line, in other words, x can be any number and y is going to be -2, so (3,-2) makes this equation be true, as does (4, -2), and so does (-5.67, -2). To find the combination of x and y that make BOTH equations true, you know already that y must be -2, because that is one of your formulas: y=-2. For the other formula to be true, you just have to figure out what x has to be when y = -2.

 

Does that help? The key bit that you were missing (I think) is that to "solve" two equations you are looking for the intersection of their lines, the place where a certain x and a certain y will make both equations be true.

-Nan