Nathanale H.

asked • 05/24/17

1. find the equation of the line that passes through pair points in slope intercept form. (1,7) and (4,22)

I need help on this question because im struggling on it

Addy B.

1.Rise over run : y2 minus y1 / x2 minus x1 
 22 - 1 = 21  = 7  or just 7 
4-1          3      1
7= slope 
 
2. slope intercept form: y=mx+b
you choose one ordered pair to plug into the x and y so im going to use the (1,7) but you could've used (4,22) as well
so since you have your slope, you plug it into m. y=7x+b 
 
3. plug in ordered pair
the ordered pair (1,7) is what you plug into the x and y of your equation y= 7x+b
1=x;7=y
7=7(1)+b 
 
4. get "B" by itself
7=7(1)+b
7 times 1=7
7=7+b
subtract the 7 and move it to the other side and the 7 will become negative
-7+7=b
-7 +7= 0
b=0
 
5. write new equation
y=7x+0 
 
6. check to see if answer is write by plugging in the ordered pair
7=7(1)+0
7=7
 
7. plug in (4,22) into the equation y=7x+b
22=7(4)+b
7 times 4= 28
22=28+b
subtract 28 from both sides and 28 will become negative
-28 +22=-6
-6=b
y=7x+(-6)
 
8. check to see if answer is write by plugging in the ordered pair
22=7(4)+(-6)
7 times 4 = 28
22=28+(-6)
22=22
 
9. answer
y=7x+0
y=7x+(-6)
they are parallel lines so they don't meet each other at all 
 
10. for graphing these lines out, I recommend desmos.com so you can see that they are parallel
 
I hope this helped you 
 
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05/24/17

1 Expert Answer

By:

Adrian G. answered • 05/24/17

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Algebra Teacher
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Find the slope using (y2 - y1) / (x2 - x1) = (22-7) / (4-1) = 15/3 = 5  So 5 is the slope
 
Now use the slope intercept form y = mx + b, where m is the slope and b is the y intercept
 
Plug a point (1,7) for (x,y) into the slope intercept form.
 
7 = 5(1) + b
7 = 5 + b
b = 2
 
Therefore the equation is y = 5x + 2
 
You can check the answer by plugging in the given points.
 
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