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find the equation of the line that passes through (13,19) and (16,13)

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2 Answers

Hi Idk,
The equation is found first by measuring the slope of the line.
Slope is denoted by rise over run (rise/run), or y/x.
This is found by taking (y2-y1)/(x2-x1)
in the points given, x is the first value and y is the second, so x1=13, x2=16, y1=19 and y2=13.
Therefore, rise over run (slope)=
(13-19)/(16-13) = (-6/3) = -2
Furthermore, the equation of a straight line is always in the form y=mx+b, where m is the slope and b is the y-intercept (or where x=0). You can find b by plugging in either of the two points you are given in the equation 
i.e. 13=(-2)(16)+b
13= -32 +b
b= 13+32
b= 45
So the equation of the line (in y=mx+b format) is y= (-2)x + 45
You can verify that this equation is correct by plugging in x or y from the other set of values into the equation:
y= -2x + 45
y= -2(13) +45
y= -26 + 45
Hope this helps!
You have 2 equations in the form of y=mx+b that you can form with these points since you are given 2 x and y values that go together.
Equation 1: 19=13m+b
Equation 2: 13=16m+b
Using the elimination method, subtract Equation 1 from Equation 2. This gives you -6=3m. Solving for this you get m=-2.
Now replace m with -2 into 1 of the equations and solve for b.
In Equation 1, it would be 19=13(-2)+b, which simplifies to 19=-26+b and b=45
Since m=-2 and b=45, the equation is y=-2x+45.