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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