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Sagot :
We need to find the equation of the line that joins the points ( 4 , 7 ) and ( 6 , 2 )
The general equation of the line is ;
[tex]y=m\cdot x+b[/tex]where m is the slope and b is y - intercept
the slope = Rise/Run
Rise = 7 - 2 = 5
Run = 4 - 6 = -2
so, the slope :
[tex]m=\frac{5}{-2}=-2.5[/tex]So, the equation of the line :
[tex]y=-\text{2}.5x+b[/tex]Using any point from the given points to find the value of b
So, using ( 4 , 7 )
when x = 4 , y = 7
[tex]\begin{gathered} 7=-2.5\cdot4+b \\ 7=-10+b \\ b=7+10 \\ b=17 \end{gathered}[/tex]So, the equation of the line is:
[tex]y=-2.5x+17[/tex]
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