Can someone help me on some geometry problem?!?

Question

my parents are not very good at math and i was just wondering that someone can help on with a little bit of something. OK here goes.

The question is" Use substition to determine whether the point is on the line. it's" y=x+1;a(1,0). anyone give an example of how to do it. Thanks!

Answer 1

substitution just means that you plug in the x and y values from the given coordinate into the equation of the line, and if the resulting statement is true, then you know that the point is on the line. so in your case:

the given point is (1,0) where 1 is the x value and 0 is the y value, so all you have to do is plug these values into y=x+1 and see if it is true so:

0=1+1 which is 0=2 which is clearly not a true statement, so therefore

the point is NOT on the line

hope that helps :)

Answer 2

Sure, no problem.

This is the principle being tested here: for an equation to be valid, the left and right hand side of the equation (what's to the left of the equal sign and what's on the right of the equal sign) must be exactly equal.. this may seem trivial to say, but that's what the equal sign means.  At all times, the number(s) and variable(s) on the left exactly equal the number(s) and variable(s) on the right.  

So (1,0) is an ordered pair, where the first number is the x coordinate, and the second number is the y coordinate.  So to see if that point is on the line, you simply plug in those numbers for their proper variable, and see if the equation still makes sense.  Here's what I mean:

for x = 1 and y = 0, let me substitute:

0 = 1 + 1

0 = 2

Is this true?  No, of course 0 is not equal to 2, but more importantly, refer to what I said in the first paragraph: what's on the left side does not equal what's on the right side, so either the equation is wrong, or the point does not fit in that equation.  Since you were given the equation, then you can assume it's correct, and the point is wrong (i.e. does not fit the equation, so it is not on the line).

So the answer is no, it is not.  If the answer would have been 2 = 2, 1 = 1,  154= 154... any solution where the left side equaled the right side (the number does not matter), then the point would be on the line.  I hope that makes sense.

Hope this helps.

Answer 3

x is the first element of the ordered pair, y is the second

Put x=1, y=0 inot the line equation:

0 = 1 + 1 ?

0 = 2 ?

The point is not on the line.

Answer 4

When you have an ordered pair like (1,0), what you have is a point on the cartesian plane. The firs number is on the X (or horizontal) axis and the second number is on the Y (or vertical) axis, like this: (x,y). To find out if a point is on any line all you have to do is substitute the values of x and y on the equation of the line. For example:

     y=x+1

     0=1+1

     0=2

Since the equation is not true, the point in not on the line. Only ordered pairs that satisfy the equation (make it true) belong to a point that's on the line. For example (3,4):

     y=x+1

     4=3+1

     4=4

So this point actually is on this line.

Algebra is pretty easy once you get the hang of it, practice a lot and you will do great in your tests.

Answer 5

(1,0) = (x,y)

x=1

y=0

0=1+1

0=2

since that is never true then the point is not on the line.

Answer 6

(1,0) means x=1, y=0

All you have to do is to replace those into the equation to see if the left hand side (LHS) equals the right hand side (RHS)

LHS

= y

= 0

RHS

= x + 1

= 1 + 1

= 2

Since LHS is not equal to RHS, point a(1,0) doesn't lie on the line.

Answer 7

Hi there...just to add to what others have said:

A line is the connection of infinite points right? So if you have an equation (graphically represents a line) then there are infinite solutions to that equation for x and y...these solutions are all of the pairs of (x,y) co-ordinates that fall on the line (ie. the points that make up the line)...so if you need to test whether a pair of (x,y) co-ordinates falls on the line (given by the equation), then you substitute the given co-ordinates for x and y into the equation and if they satisfy the equation (meaning that the equation stays true ie. if you end up with something like 2=2 then they satisfy but if you end up with -13 = 7 then they don't) then the point is on the line.

So to test if (1,0) falls on the line we make the substitution x=1 and y=0 into the given equation y=x+1 and get:

0 = 1 + 1

0 = 2

which is not true so the point does not fall on the line y=x+1.

Note: You must remember that the first co-ordinate in an ordered pair always represents the x co-ordinate and the second represents the y co-ordinate -------> (x,y).

Hope it helps (^_^)