If we want to graph a horizontal line, we will do the following: y = 0x + 3 No mat

beuz89100g6c

beuz89100g6c

Answered question

2022-02-23

If we want to graph a horizontal line, we will do the following:
y=0x+3
No matter the domain for x, the range for y will always be 3. Therefore, we have a horizontal line.
y=0(0)+3=(0,3)
y=0(1)+3=(1,3)
y=0(2)+3=(2,3)
Now the formula to graph a vertical line looks like this:
x=3
Well, wait a second. Where is the y? I would like to see the y in the equation. But it is missing. How can I write the equation for a vertical line that includes the y variable? This is all I can think of:
x=0y+3
And with the following domain:
x=0(0)+3
x=0(1)+3
x=0(2)+3Is this correct? Is it ok to reverse the x and y, as I just did above? Or does this not make it a slope-intercept equation anymore? It should still be a linear equation, since the variables are raised to the first power, in my opinion. But the slope-intercept form looks like this: y = mx + b. So I am not sure if this is still a slope-intercept equation.

Answer & Explanation

Deichman82j

Deichman82j

Beginner2022-02-24Added 2 answers

No matter which form you choose your equation to a unique line will always be unique, For example
xa+yb=1
or
Ax+By=C
or
y=mx+c
or
m=yy0xx0
or
yy1=y2y1x2x1(xx1)
or
x=x0+at,y=y0+bt
Whichever form you choose it'll always lead you to a unique solution (Just sometime it'll not look similar but believe me it'll be, It's just matter of rearrangement )
dinela24k

dinela24k

Beginner2022-02-25Added 7 answers

For linear functions we have the ability to write one variable solely in terms of the other, with y being the usual dependent variable. The expression y=2x+5 is shorthand for the set {(x,y)R2y=2x+5}, points whose y coordinate is five more than twice the x coordinate; at the end of the day you're just specifying points whose coordinates meet a certain criteria. The equation x=3 simply indicates the set of points {(x,y)R2x=3}, points whose x coordinate is 3.
Also, since a linear function with nonzero slope is 1-1, it is possible to write x as a function of y:
y=mx+bmx=ybx=1mybm

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