Question

Find the equation of the line that passes through the points (2, 5) and (2, 12).

Answer 1

start by finding the slope...

change in y divided by chaneg in x

Answer 2

a 'mathlete' called 'calculus' - asking about slope intercept equation!!!

Answer 3

If you read my profile then you be clear of this "calculus" misconception.

Answer 4

@MrNood

Answer 5

(2, 5)
(2, 12)

I know that is an undefined slope but I don't know how to put this as an equation.

Answer 6

OK

Do you recognise the 'slope intercept ' form of the linear equation

y=mx+b

??

Answer 7

Yes

Answer 8

I got the slope as 0 because \(\large \frac{7}{0} = 0\).

Answer 9

Undefined slopes have the same x value?

Answer 10

that's correct... so what's the equation..?

Answer 11

I got the y-int as 5 because:
\(\large 5 = 0(0) + b\)
\(\large 5 = 0 + b\)
\(\large 5 = b\)

Answer 12

So I guess that the equation should be like:
\[\large y = 0x + 5 \]
which i believe can equal to
\[\large y = 5 \]

Answer 13

On the plane, we can define the "line" as the set of points whose change in y over change in x gives a constant called "slope".
This slope is also defined as the angle of the line respective to the x-axis:

so, in orer to calculate this angle, we can use the tangent, so therefore:
\[m=tg (\alpha)\]
and "slope" is also defined by two points, so we can define two points \(a(x_a,y_a)\) and \(b(x_b,y_b)\) and some play with the intervals, we obtain :
\[tg (\alpha) = \frac{ y_b - y_a }{ x_b - x_a }\]
So therefore, the slope must be defined by the equation:
\[m=\frac{ y_b - y_a }{ x_b - x_a }\]

Answer 14

what is true about the X value for ALL y values?

Answer 15

just plot the points