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How To Write Linear Equations Using The Point Slope Formula
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Feb 19, 2025
In my April 28th Prealgebra lesson , I taught my students how to write equations of linear functions using the point slope Formula. This can be a daunting task so I tried to simplify it for them.
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So today we're going to talk about how
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to write linear equations and this is
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prealgebra now a lot of students
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struggle with the point slope uh formula
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I don't like to teach that one so I try
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to teach a better method so first thing
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we need to know is what is a linear
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equation again a linear equation is an
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equation that when you graph it it forms
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a line this is why we call it linear
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linear line all right so every linear
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equation
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can be written as y = mx + b where m is
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the slope I don't know why we choose the
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we chose the letter M instead of s so
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the slope is M and then B is called the
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Y intercept now the Y intercept is where
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the line crosses the Y AIS on a set of
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axis okay so so any SL any linear
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equation can be written as y = mx + b so
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that's where you start now we in my
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class we've talked about how to find
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slopes we spent the last couple of weeks
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doing the rate of change then slop so my
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students know how to find the slope now
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here this is a pretty simple and basic
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um problem in this problem we are asked
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to write the equation of a line given
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the slope and the Y intercept now this
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is pretty basic stuff so once you know
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the slope and the Y intercept you know
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that any line is in the form y = mx + b
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so if you were to write right this will
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be y = NX the slope is 12 so all you
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have to do is just do a clear
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substitution so 1/2 is the slope x + B
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now because this is -5 some people go
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plus5 you can do that but at this point
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we know that the positive and the
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negative gives you negative so you don't
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have to go baby steps you can just go
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ahead and say this is 12 x - 5 all right
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now I give you a second example here
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where the slope is two and Y intercept
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is 1/3 so to write this equation again
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is the same process y = NX m is your
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slope so this is 2 x + 1/3 all right so
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again these two examples are pretty
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basic now in this second example here
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now we have to write an equation given
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two points so how do you do that again
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in this example we're going to use uh 48
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and then -25 so there's two steps to it
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all right so we've been given two points
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and we want to find the equation of the
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line given two points so my students
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again know how to find the slope we use
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our basic formula Y2 - y1 over X2 - X1
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so basically they know that this is the
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formula to find the slope so when you're
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given two points all you have to do is
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just label them so we put a label on top
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of these so this is X1 y1 and this is X2
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and Y2 these are two coordinate of two
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separate points all right so now to find
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the slope you have to be extremely
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careful sometimes people put n = Y2 - y1
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X2 - X1 and when when they do the
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subtraction they they get the wrong
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thing they they subtract five from four
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instead of five from8 so you have to
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make sure you respect the order okay so
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if you go Y2 - y1 you have to go X2 - X1
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you can't have Y2 - y1 over X1 - X2 it's
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going to give you the wrong answer all
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right so in this case X1 is 4 y1 is 8
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and here X2 is -2 Y2 is 5 so Y2 - y1
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will be = 5 - 8 which we have here and
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then X2 - X1 will be -2 - 4 so 5 - 8 is
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-3 and then -2 - 4 is6 so you have to
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know your basic subtraction and your
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basic arithmetics if you don't know how
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to subtract number or add numbers you're
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going to have a hard time in this
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section so -3 over -6 we've worked on
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simplifying fractions that give you one
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/ two all right now step two we have to
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find the Y intercept now here's what I
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do here so I don't like to use the point
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slope form that one is so confusing to
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the students so I keep it very simple so
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now we have this equation here y = 12x +
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B because we found the slope so all we
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have to do now is solve for the Y
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intercept so the way you do it is is you
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pick one of those because these two
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points form the line that means those
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points belong on the line right so you
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can choose either one of those you can
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need to choose this one or this one and
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then plug it in for x and for y to solve
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for b so here we're going to replace X
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by 4 and Y by 8 and we're going to solve
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for b which is the Y intercept so I'm
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going to go
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8 = 12 * 4 + b is
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8 12 * 4 my students know they have to
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put a one under that so this is 1 * 4
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which is 4 4 over 2 that is 2 plus b
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right and then we solve for b we have we
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have to subtract -2 -2 so therefore B is
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equal 6 and now our equation is complete
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okay so
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y
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equal 12 x + 6 because of Y intercept is
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6 so basically
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this is how I teach my students how to
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find the equation of a linear equation
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given two points hope this helps you
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guys out if you have any questions leave
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a message under this thanks for watching
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