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y = -1 (x - 6)
Explanations:The point - slope form of the equation of a line is:
[tex]y\text{ - y}_1=m(x-x_1)[/tex]Where m represents the slope, and can be calculated using the equation:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]The line passes through the point (6, 0) and (0, 6)
[tex]\text{This means that x}_1=6,y_1=0,x_2=0,y_2=6[/tex]Calculating the slope using the formula given above:
[tex]\begin{gathered} m\text{ = }\frac{6-0}{0-6} \\ m\text{ = }\frac{6}{-6} \\ m\text{ = -1} \end{gathered}[/tex]Substituting the values of m, x1, and y1 into the point slope form of the equation of a line:
y - 0 = -1 (x - 6)
y = -1 (x - 6)