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I have no idea how to do this at all, I am trying to study before I take calculus again.

I am supposed to find equations for the line that passes through the point $(2, -5)$ and:

  1. Has slope $-3$.
  2. is parallel to the x-axis.
  3. is parallel to y axis
  4. parallel to the line $2x-4y = 3$

Is this kind of information important to calculus? I am not familiar with any of the terms I am seeing and I don't remember doing anything similar to this in class. It seems like it is so rarely used that it is near impossible to remember all these small things.

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    You might find [Khan Academy](http://www.khanacademy.org/#algebra) useful for seeing problems explained as they are solved.2012-01-01

2 Answers 2

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What formulas do you know for finding equations of lines? There are a couple of standard ones:

  • Point-slope. If you know a point $(a,b)$ through which the line goes and the slope $m$ of the line, then the equation of the line is given by $y-b = m(x-a)$.

  • Two-points. If you know two points $(a,b)$ and $(c,d)$ that are on the line, then:

    • If $a=b$, the line is vertical, and the equation is $x=a$.
    • If $a\neq b$, then the slope of the line is $m = \frac{\text{rise}}{\text{run}} = \frac{d-b}{c-a}.$ Now use the point-slope formula with $(a,b)$ and $m$.
  • Slope-intercept. If you know the slope $m$ and the $y$-intercept $(0,b)$, then you are actually in a "point-slope" situation, with the point $(0,b)$. So the equation is just $y-b=mx$, or $y=mx+b$.

The first problem, you know a point on the line and the slope of the line. The point-slope formula gives you exactly what you want.

In the second problem, you know a point, and you are implicitly told the slope: "parallel to the $x$-axis" means that the line has to be horizontal. What is the slope of a horizontal line?

Same in the third problem: "parallel to the $y$-axis" means the line has to be vertical. The equations of vertical lines are always of the form $x=k$ for some constant $k$. If the line has to go through $(2,-5)$ and be vertical, what is the equation?

And in the fourth problem, you are again given the slope implicitly: "parallel to $2x-4y=3$" means "having the same slope as $2x-4y=3$". Find the slope of the line $2x-4y=3$ and proceed form there.

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    I try and understand why, I don't know what is wrong with me, but I can never remember I always forget no matter how much practice I do.2012-01-01
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Hint: Every line can be written as $y = mx + b$, where $m$ denotes the line's slope and $b$ denotes its $y$-intercept. For each of your conditions (which are four separate problems), you are given the value of $m$ (the slope). You can plug in the other point $(2, -5)$ and solve for $b$.

Here is how you might work the first one. Since the slope of the line is $-3$, you know the equation looks like $ y = -3x + b. $ To determine $b$, plug in the point you know about. $ -5 = -3 \cdot 2 + b. $ Some algebra reveals that $b = 1$. Thus, the equation for the line is $ y = -3x + 1. $

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    y=mx+b is all I have memorized for this but I couldn't make it work.2012-01-01