Alrighty. So, the topic of this blog is how to write an equation when you have two points. So let's begin.
Lets say you have a point of (7,-2) and a point of (3,-1). So, the equation, known as the slope-intercept form, is written like this: y-y1=m(x-x1). First of, lets establish what this means and what it stands for. M represents the slope of the line, just like the equations y=mx+b. Alright, so lets move on. The y and the x without the ones next to them stay the same when you're plugging in numbers, however the y1 and x1 is where you plug in one of the coordinates or points that you have.
So, lets figure out how to do that equation now... *Note*
(7,-2) (3,-1) to find the slope: y2-y1
y-y1=m(x-x1) x2-x1
Slope= -1-(-2)= 1
3-7 -4
So, y-(-2)= (-1/4)(x-7)
y+2= (-1/4)(x-7) *Parenthesis= multipication
y+2= (-1/4x)+7/4 or y+2= -.25x+1.75
Now, like every equation, you want y alone. Therefore, on this equation, you will subtract the 2 on both sides the get y by itself.
y=-.25x+(1.75-2)
y=(-.25x)-.25
And that is how you write an equation in y-intercept form.
Lets say you have a point of (7,-2) and a point of (3,-1). So, the equation, known as the slope-intercept form, is written like this: y-y1=m(x-x1). First of, lets establish what this means and what it stands for. M represents the slope of the line, just like the equations y=mx+b. Alright, so lets move on. The y and the x without the ones next to them stay the same when you're plugging in numbers, however the y1 and x1 is where you plug in one of the coordinates or points that you have.
So, lets figure out how to do that equation now... *Note*
(7,-2) (3,-1) to find the slope: y2-y1
y-y1=m(x-x1) x2-x1
Slope= -1-(-2)= 1
3-7 -4
So, y-(-2)= (-1/4)(x-7)
y+2= (-1/4)(x-7) *Parenthesis= multipication
y+2= (-1/4x)+7/4 or y+2= -.25x+1.75
Now, like every equation, you want y alone. Therefore, on this equation, you will subtract the 2 on both sides the get y by itself.
y=-.25x+(1.75-2)
y=(-.25x)-.25
And that is how you write an equation in y-intercept form.