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the equation for The line that passes through (-3, 5) and (-2, -6)

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2 Answers

Hi Anthony;
You stated "the equation".  I am assuming that your instructor wants standard equation.
(-3, 5) and (-2, -6)
The first thing we need to do is establish the slope of the line.  Slope is defined as the change-of-y divided by the change-of-x...
(y-y1)/(x-x1)
(5--6)/(-3--2)
(5+6)/(-3+2)
11/-1
-11
The standard format of an equation is...
Ax+By=C, neither A nor B equal zero and A is greater than zero.
slope=-A/B
slope=-(-11/1)
slope=11/1
11x+1y=C
11x+y=C
Let's plug-in one point to establish C...
(-3, 5) and (-2, -6)
11x+y=C
[11(-3)]+5=C
-33+5=-28
Let's verify with the other point...
[11(-2)]+-6=C
-22-6=c
-28=c
11x+y=-28
Hi Anthony!
 
To write an equation for a line given two points, you can:
1. Find the slope.
2. Use the slope and a given point to write the equation in point-slope form.
3. Solve for slope-intercept form if that is necessary.
 
Here's how you do it for this problem:
1. Find the slope using slope formula ("rise over run"):
m = rise/run = (y2 - y1)/(x2 - x1)
 
For this problem:
(x1, y1) = (-3,5)
(x2, y2) = (-2,-6)
 
Plug those values into slope formula:
m = (-6 - 5)/(-2 - (-3))
Watch your signs and simplify:
m = (-11)/(1) = -11
So, your slope is -11.
 
2. Now, you can write the line equation in point-slope form, which looks like this:
y - y1 = m(x - x1)
 
Plug in the slope you found, and one of the given points. I'll use (-3,5), but you can use either.
 
y - 5 = -11(x - (-3))
y - 5 = -11(x + 3)
That is the equation in point-slope form.
 
3. You can then simplify to slope-intercept form, y = mx + b.
Use the point-slope form, and solve for y ("get y alone on one side of the equals sign"):
 
y - 5 = -11(x + 3)
y - 5 = -11x - 33
y = -11x - 33 + 5
y = -11x - 28
 
In slope-intercept form, your answer is:
y = -11x - 28
 
Hope this helps!