Question 202337: Algebra 2: How do i find an equation with the given slope and points for example : Slope = -2: passing through (3, -1)
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! 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. :-)
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