Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
You are actually trying to find four equations for four different lines. You do realize that, right? –  Arturo Magidin Jan 1 '12 at 20:37
Yes, I will edit to make that more clear. –  user138246 Jan 1 '12 at 20:42
You might find Khan Academy useful for seeing problems explained as they are solved. –  Austin Mohr Jan 1 '12 at 21:00

2 Answers 2

up vote 2 down vote accepted

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.

share|improve this answer
How can I find the slope of an equation if I don't know what the (a,b) and stuff are supposed to be in their equation? –  user138246 Jan 1 '12 at 20:47
@Jordan: Equations don't have slopes. Lines (and, in calculus, graphs of functions at specific points) have slopes. I don't understand your question: you are given the point, and you are being given enough information to find the slope. What is the problem? –  Arturo Magidin Jan 1 '12 at 20:49
I don't know how to manipulate the equation $2x-4y=3$ in a way to make it into a line of the form y=mx+b I am getting nonsensical answers that do not match what the book has. –  user138246 Jan 1 '12 at 20:50
@Jordan: $2x-4y = 3$ is the same as $2x=3+4y$, which is the same as $2x-3=4y$, which is the same as $4y=2x-3$, which is the same as $y = \frac{1}{4}(2x-3)$, which is the same as $y = \frac{2}{4}x - \frac{3}{4}$, which is the same as $y=\frac{1}{2}x - \frac{3}{4}$. So $m=\frac{1}{2}$. –  Arturo Magidin Jan 1 '12 at 20:52
The book gets $y=1/2x-6$ and I can't figure out how. –  user138246 Jan 1 '12 at 20:54

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 $$ y = -3x + 1. $$

share|improve this answer
y=mx+b is all I have memorized for this but I couldn't make it work. –  user138246 Jan 1 '12 at 20:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.