Write an equation of a line with undefined slope that passes through the point(3,-2)

BOSEOK
Sep 17, 2017

#3**+1 **

The slope of a horizontal line *is* well defined- it is zero.

I think what is wanted is as follows:

General equation of a straight line is y =mx + c

Here we know that this line goes through point (3, -2) so we can say

-2 = m*3 + c

This means c = -2 - 3m. Put this in the equation for the line:

y = mx - 2 - 3m

or

y = m(x - 3) - 2

The slope m is undefined.

Alan
Sep 17, 2017

#5**0 **

To put it simply, in linear equations, if an equation is y= (any real number), then it is horizontal. For example, y=2 is horizontal, and it has an undefined slope. x=3 is actually a vertical line. Its slope is 0.

Correct me if I'm wrong.

Gh0sty15
Sep 17, 2017

#6**+1 **

BOSEOK is correct; the equation is x=3.

Contrary to what Gh0sty stated, the slope is defined when a linear function happens to be horizontal. Let's figure out the slope of the graph provided by Gh0sty. I will use the points \((3,-2)\) and \((0,-2)\). Let's find the slope.

Of course, the formula for slope is the following:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{-2-(-2)}{0-3}\) | Continue to simplify the fraction. |

\(m=\frac{0}{-3}=0\) | |

The slope is 0. 0 is a valid number for the slope. If you type into Demos y=0x-2, the line will appear exactly as the picture above.

Let's try calculating the slope of the line x=-3. Two arbitrary points on the line are \((-3,2)\) and \((-3,0)\)

What is the slope of this? Let's try using the formula again. Let's see what happens.

\(\frac{0-2}{-3-(-3)}\) | Simplify both the numerator and the denominator. |

\(\frac{-2}{0}\) | |

Of course, any number divided by 0 is undefined and therefore it has an undefined slope.

Therefore, BOSEOK's answer is correct because it meets both criteria of

1) A line with an undefined slope

2) A line that passes through the point \((3,-2)\)

And therefore, \(x=3\) is correct.

TheXSquaredFactor
Sep 17, 2017