Thread: Equations 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?

This is not hard, all that you need is the point-slope formula, which states that



& 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 (for the problem #5).

I personally like 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:














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




this can also be written as:


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.