SOLUTION: This is another one I don't undersrtand. In order to write the equation (in slope intercept form) of the line passing through the points (3,1) and (4,2) I have to graph it right?

Algebra ->  Graphs -> SOLUTION: This is another one I don't undersrtand. In order to write the equation (in slope intercept form) of the line passing through the points (3,1) and (4,2) I have to graph it right?       Log On


   

Question 86894This question is from textbook
: This is another one I don't undersrtand. In order to write the equation (in slope intercept form) of the line passing through the points (3,1) and (4,2)
I have to graph it right?
I need a step-by-step on that too.
Thanx

This question is from textbook

Found 2 solutions by jim_thompson5910, dolly:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (3,1) and (4,2)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (3,1) and (x%5B2%5D,y%5B2%5D) is the second point (4,2))


m=%282-1%29%2F%284-3%29 Plug in y%5B2%5D=2,y%5B1%5D=1,x%5B2%5D=4,x%5B1%5D=3 (these are the coordinates of given points)


m=+1%2F1 Subtract the terms in the numerator 2-1 to get 1. Subtract the terms in the denominator 4-3 to get 1



So the slope is

m=1





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-1=%281%29%28x-3%29 Plug in m=1, x%5B1%5D=3, and y%5B1%5D=1 (these values are given)



y-1=1x%2B%281%29%28-3%29 Distribute 1


y-1=1x-3 Multiply 1 and -3 to get -3%2F1. Now reduce -3%2F1 to get -3

y=1x-3%2B1 Add 1 to both sides to isolate y


y=1x-2 Combine like terms -3 and 1 to get -2

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Answer:



So the equation of the line which goes through the points (3,1) and (4,2) is:y=1x-2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1 and the y-intercept is b=-2


Notice if we graph the equation y=1x-2 and plot the points (3,1) and (4,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=1x-2 through the points (3,1) and (4,2)


Notice how the two points lie on the line. This graphically verifies our answer.

Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!
You do not have to graph it.
Given points are (3,1) and (4,2)
Slope of the line through these points is difference in y values/difference in x values
So slope = (2-1)/(4-3)
= 1/1
= 1
Slope point form is y - y1 = m(x - x1) where 'm' is the slope and (x1,y1) is the point through which the line passes.
Considering (3,1) to be (x1, y1) the equation would be :
y - 1 = 1(x - 3)
==> y - 1 = x - 3
==> y = x - 3 + 1
==> y = x - 2
This is of the slope intercept form y = mx + c