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Answer :

Given points

[tex]L(5,0)\text{ and M\lparen0,5\rparen}[/tex]

Solution

Firstly, find the slope

Slope Formula

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now

[tex]\begin{gathered} x_1=5 \\ x_2=0 \\ y_1=0 \\ y_2=5 \end{gathered}[/tex]

Plug in into the formula

[tex]Slope\text{ \lparen m\rparen=}\frac{5-0}{0-5}=\frac{5}{-5}=-1[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=-1(x-5) \\ y=-x+5 \\ \end{gathered}[/tex]

The standard form is

[tex]x+y=5[/tex]

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