SOLUTION: Write an equation in general form for the line that goes through (4, -1) and (4,5) x=? Thank you for your help.

Question 233668: Write an equation in general form for the line that goes through (4, -1) and (4,5)
x=?

Thank you for your help.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The points are (x,y) = (4,-1) and (4,5)

slope-intercept form of the line is y = mx + b where m is the slope and b is the y-intercept.

It appears you will have a vertical line.

Let's see what happens:

Slope is equal to (y2-y1) / (x2-x1)

(x1,y1) = (4,-1)
(x2,y2) = (4,5)

y2-y1 = 5 - (-1) = 6
x2-x1 = 5 - 4 = 0

(y2-y1) / (x2-x1) becomes 6/0 which is undefined.

This means that y can vary but x can't, so the line is vertical.

The equation of your line is x = 4

x will always be 4 and y can be any value.

How did this equation come about?

The standard form of the equation of a straight line is ax + by = c

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

To convert the standard form to the slope-intercept form, you do the following:

Equation is:
ax + by = c
Subtract ax from both sides to get:
by = -ax + c
divide both sides by b to get:
y = -ax/b + c/b

That's the same as the slope-intercept form of the equation of y = mx + b where m = the slope = (-a/b).

If b = 0, the slope is undefined.

If b = 0, the standard form of the equation of:

ax + by = c becomes:

ax + 0y = c which becomes:

ax = c

In your equation, a = 1 and c = 4 to get:

x = 4

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