SOLUTION: Problem goes as follows: "Graph the line x=4" the answer provided is as follows: (4,-5)(4,-1)(4,7). I do not understand how this answer was discovered. I am in dire ne

Question 249138: Problem goes as follows:
"Graph the line x=4"
the answer provided is as follows:
(4,-5)(4,-1)(4,7).
I do not understand how this answer was discovered. I am in dire need of your assistance. Any help is immensely appreciated! Thank you.
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The points (4,-5)(4,-1)(4,7) have what in common? They have the value of 4 as the x coordinate. So we'll get a vertical line.

If you plot those points you get

and draw a straight line through them, you get

So the graph of is the vertical blue line. Basically, the value of 'x' is fixed at 4 (ie it cannot be any other value), but y can be any value which gives us this vertical line.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = 4 is a vertical line.

the slope is undefined because there is never a change in the value of x for a change in the value of y.

the slope of the equation is (y2-y1) / (x2-x1)

x2 and x1 are the same so the denominator of the equation is 0 which leads to an undefined slope because division by 0 causes the result to be infinity which is an undefined number.

the standard form of the equation for a straight line is:

ax + by = c, where:

a = the coefficient of the x term
b = the coefficient of the y term
c = the constant.

you can convert the standard form of the equation to the slope intercept form by doing the following:

ax + by = c
subtract ax from both sides to get:
by = -ax + c
divide both sides by b to get:
y = (-a/b)*x + (c/b)

that's the slope intercept form of the equation of a straight line.
(-a/b) = the slope of the line, called m.
(c/b) = the y-intercept of the line, called b

the slope intercept form of the equation is called y = m*x + b, where:

m is the slope
b is the y-intercept.

In the standard form of the equation or:

ax + by = c,

if b = 0, then the equation becomes:

ax = c, because the y terms drops out (anything multiplied by 0 equals 0).

Because the y term drops out of the equation, the value of y is not constrained to be anything special in relationship to x.

It is not limited by the rules of the equation.

this means that y can be anything, but x has to be what the equation says it has to be.

when you graph the equation, you are plotting the value of x in relation to the value of y.

x = 4 means that the value of x has to be equal to 4.

y not in the equation means that y is free to be any value it wants.

this is what creates the vertical line.

when you plot the equation of a vertical line, you can see that the value of x has to be 4.

you can also see that, along that line, the value of y can be any value.

that is why your solution showed you (4,a), (4,b), (4,c), etc.

there was no equation to force the selection of y given a specific value of x.

for example, if the equation was y = 4x, then when x = 1, y has to be 4*1 and could be nothing else.

In the example x = 4, there is no such restriction for the value of y, meaning the value of y could be anything, but the value of x had to be 4.

when you plot the line you will see that it is a vertical line on the graph.

the requirements of the equation are that x = 4.

there are no requirements on the value of y, so pick any value of y when x = 4 and create your vertical line.

if your equation was y = 5, then you would have a horizontal line.

this might be easier for you to see.

In that case, x can be any value and y always has to be 5, regardless of the value of x.

x = 4 is the same concept. y can be any value and x always has to be 4, regardless of the value of y.

the only difference is, that in the case of y = 5, the slope is equal to 0, while in the case of x = 4, the slope is undefined (division by 0 caused undefined).

look at the standard form of the equation again:

ax + by = c.

when b = 0, y drops out of the equation, and when a = 0, x dropes out of the equation.

you get:

ax = c when y drops out.

you get:

by = c when x drops out.

since the slope is (-a/b), when b = 0, the slope is undefined because you are dividing by 0, and when a = 0, the slope is 0 because you are dividing into 0.

best answer I can give. i don't know how to explain it any other way.

the answer is:

since you are plotting a graph of y in relationship to x, since y is not in the equation, y can be any value as long as x = 4 because the only constraint in the equation is that x = 4. y, not being in the equation, has no constraints. you are free to pick any value of y as long as x = 4.

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