y=5 on a graph

[jolly cradle]

Why does it look like that and not undefined?

Why is it undefined and not zero

Also I have another question.
y=x-6
What does x mean?? How do I graph this?

[brisk obsidian]

y=5 is just a line because no matter what the value of X is at a point, the y coordinate is always 5

[brisk obsidian]

you graph this by plotting points, the X can be found on the horizontal axis

substitute in X=0 and you have y=-6
(0,-6) sub in X=1 and you have y=-5
(1,-5) and so on

or you can plot it on the following knowledge:
a constant (anything not multiplied by X) will be the point at which the graph will intersect the y axis when x=0
the coefficient (whatever is multiplying x) shows the slope of the graph, aka how far up the graph goes if you move 1 to the right

[jolly cradle]

So if it was
Y=5x
Start at 0,0 up/down 5 right/left 1

[brisk obsidian]

up 5 for every 1 to the right, down 5 for every one to the left

yes

[jolly cradle]

Ok

[jolly cradle]

Undefined is for y
Zero is for x
Up and down is y
Left and right is x

Y=5
5 is y intercept…
Right?

If there is no x and only y intercept it’s undefined not zero

[brisk obsidian]

no

it's just a line

it has a slope of 0

[jolly cradle]

Line = zero?

[brisk obsidian]

because it's the equivalent of this:
y=0x+5

no matter what x is, it's always multiplied by 0 so y will always be 5

[jolly cradle]

So y intercept by itself is zero not undefined
X=5 would be 5 undefined

[brisk obsidian]

X=5 has an undefined gradient yes

but it's still just a line

itself isn't undefined

[jolly cradle]

Gradient?

[jolly cradle]

???

[brisk obsidian]

gradient is another word for how much it goes up for every 1 it goes across

[brisk obsidian]

X=5 is a line that is defined to have all coordinates satisfying (5,y) lie on that line

[bitter wigeon]

@jolly cradle The formula for gradient aka slope of a line is (y_2 - y_1)/(x_2 - x_1), where (x_1, y_1) and (x_2, y_2) are points on the line. When the line is y = 5, the numerator is always 0, so the slope is 0. When the line is x = 5, the denominator is always 0, and you can't divide by 0, so undefined.

[jolly cradle]

Thank you guys