Question 202337
Algebra 2: How do i find an equation with the given slope and points for example : Slope = -2: passing through (3, -1)


I'm not very good with making formulas look good on this website yet so when I say x1, I mean "x" subscript 1.  Similarly, when I say y1, I mean "y" subscript 1, k? :-)


Now that you know that, let's begin.  


When you know the slope and a point that the line goes through, you can find the equation of the line by using the POINT SLOPE equation of a line.  Here it is:


y - y1 = m(x - x1)



All you have to do is fill in the info you have.  In this case, you know the slope is -2.  In the above equation, "m" refers to slope, so that means:  
m = -2.


The line passes thru the point (3, -1)    The number 3 is your x1 and the number -1 is your y1.  All you have to do now is "plug" in the values for your variables.  So let's do that now:


Remember:  m = -2
Passes thru (3, -1)


POINT SLOPE equation of a line:  y - y1 = m(x - x1)

y - (-1) = -2(x - 3)
y + 1 = -2(x - 3)  


See where I plugged in the slope and the x1 and y1 values?   Sometimes the problem ends there, but other times, you have to put the equation in the SLOPE INTERCEPT form of a line, which is y = mx + b.  Sooooo, if you are supposed to do that, you need to solve for y and you'll be fine.  Let's try that now by taking the first few steps above and doing some more calculations..........



y - (-1) = -2(x - 3)
y + 1 = -2(x - 3)  
y + 1 = -2x + 6  (Distributed the -2)
y = -2x + 6 - 1  (Subtracted 1 from both sides)
y = -2x + 5  



Now you have the answer in slope/intercept form.  


I hope this is helpful. :-)