Find the equation of the line that contains the given point and has the given slope:

Point (5,1), m= 2/3

Point (1,5), m = -4/5

Point (0,0), m = 3/4

Point (2,0), m = 5/6

Point (-2,5), slope is undefined

Point (-3,5), m = 3

help?:eek:

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- Nov 1st 2007, 01:52 AMsgw89Equations and Given Points in Slopes
Find the equation of the line that contains the given point and has the given slope:

Point (5,1), m= 2/3

Point (1,5), m = -4/5

Point (0,0), m = 3/4

Point (2,0), m = 5/6

Point (-2,5), slope is undefined

Point (-3,5), m = 3

help?:eek: - Nov 1st 2007, 02:20 AMKrizalid
This is not hard, all that you need is the point-slope formula, which states that

$\displaystyle y-y_1=m(x-x_1).$

$\displaystyle (x_1,y_1)$ & $\displaystyle m$ are the point and the slope respectively, so plug the values into the aforesaid formula.

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When the slope is undefined, the equation which represents the line is $\displaystyle x=-2$ (for the problem #5). - Nov 1st 2007, 03:42 AMangel.white
I personally like $\displaystyle y=mx+b$ better (prob b/c thats how I learned it)

y = y value

x = x value

m = slope

b = y-intercept

If you want to use this format, the first one would go like this:

Given: Point (5,1), m= 2/3

plug in:

$\displaystyle y=mx+b$

$\displaystyle 1=\frac{2}{3}(5) + b$

$\displaystyle 1=\frac{10}{3}+b$

$\displaystyle 1 - \frac{10}{3} = b$

$\displaystyle \frac{3}{3} - \frac{10}{3} = b$

$\displaystyle \frac{3-10}{3} = b$

$\displaystyle \frac{-7}{3} = b$

Now our slope and y-int are constants, so we just plug them into our equation:

$\displaystyle y=mx+b$

$\displaystyle y=\frac{2}{3}x+\frac{-7}{3}$

this can also be written as:

$\displaystyle y=\frac{2}{3}x-\frac{7}{3}$

You can then use this equation to take any x value and find the y value, or any y value and find the x value, or you could take any x, y pair and with the given slope, find the y-intercept. Or any x, y pair and with the given y-intercept you could find the slope.

We leave x and y as variables because while the slope and y-intercept are constants, there are an infinite number of x and y values which will satisfy this equation (any point on the line will have an x,y pair that will satisfy the equation). For example, you will notice that when x=8 and y=3, the equation works out as well. And we plug in the values for m and b because these are constants, they will never change no matter what part of the line you are looking at.