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find the slope of the line that passes through (1,6) and (9,3)

Sagot :

Given the points ( 1 , 6 ) and ( 9 , 3 )

The slope of the line = m

[tex]m=\frac{rise}{run}=\frac{3-6}{9-1}=\frac{-3}{8}[/tex]

so, the equation will be :

[tex]y=-\frac{3}{8}x+b[/tex]

where b is a constant, we will find the value of b using the point ( 1 , 6 )

when x = 1 , y = 6

so,

[tex]\begin{gathered} 6=-\frac{3}{8}\cdot1+b \\ b=6+\frac{3}{8}=\frac{51}{8} \end{gathered}[/tex]

so, the equation of the line is:

[tex]y=-\frac{3}{8}x+\frac{51}{8}[/tex]

The standard form of the line will be as following:

Multiply the equation by 8

So,

[tex]\begin{gathered} 8y=-3x+51 \\ \\ 3x+8y=51 \end{gathered}[/tex]

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