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Ok one more, write an equation in slope-intercept form for the line that passes through the points (0,3)and (3'-5)

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2 Answers

There's a couple of ways you can solve this.  I'll show you the way I prefer, but your mileage may vary.

First (and this is true in every method), to find the equation of a line you absolutely need the slope.  They'll either give you the slope or, like in this case, they'll give you two points.  With two points you find the slope with this equation:

m=(y2-y1)/(x2-x1)

Or, colloquially:

m= Rise/Run

Don't worry about which of your x's is x1 or which is x2.  It's arbitrary.  The important point is that you be consistent.  (3-(-5))/(0-3) is the same as ((-5)-3)/(3-0).  Your slope here is -8/3.

Now, using my method, let's plug our slope into the equation for slope-intercept:

y=mx+b  becomes y=(-8/3)x+b

We just need to find B.  Pick either of the two points you're given (I'm going to go with (0,3) because it has a 0 which makes the math easier) and plug the numbers in and solve for B.

3=(-8/3)(0) + b

b=3

Since b=3 we can plug that number in for b, giving us the equation

y=(-8/3)x+3.

If you have time on your test, plug in both points into this equation to confirm it comes out true.

3=(-8/3)0+3=3

-5=(-8/3)(3)+3 = -5

use and re - use the slope formula and then the point slope formula

these formulas will come in handy

slope, m = (y2 - y1) / (x2 - x1) = (-5 - 3) / (3 - 0) = -8 / 3

now you have both a point and the slope, so use the point slope formula. either point will work but choose the point with the zero in it to make manipulating the equation easier.

(y - y1) = m (x - x1)

(y - 3) = (-8/3) (x - 0)

y = (-8/3) x + 3

sniff if done correctly by cheking both points and it works.

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