Answer:
A. [tex](\frac{-1}{3},\frac{1}{3})[/tex]
B. [tex](\frac{2}{3},0)[/tex]
Slope = [tex]\frac{-1}{3}[/tex]
Step-by-step explanation:
We are given the equation of the line as [tex]3x+9y=2[/tex].
A. The co-ordinate is given by [tex](x,\frac{1}{3})[/tex]
Substituting the value [tex]y=\frac{1}{3}[/tex], we get,
[tex]3x+9y=2[/tex] implies [tex]3x+9\times \frac{1}{3}=2[/tex] implies [tex]3x+3=2[/tex] i.e. 3x = -1 i.e. [tex]x=\frac{-1}{3}[/tex]
Thus, the co-ordinate is [tex](\frac{-1}{3},\frac{1}{3})[/tex].
B. The co-ordinate is given by [tex](\frac{2}{3},y)[/tex]
Substituting the value [tex]x=\frac{2}{3}[/tex], we get,
[tex]3x+9y=2[/tex] implies [tex]3\times \frac{2}{3}+9y=2[/tex] implies [tex]2+9y=2[/tex] i.e. 9y = 0 i.e. y= 0
Thus, the co-ordinate is [tex](\frac{2}{3},0)[/tex].
Since, the slope of a line is given by [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
We get,
Slope = [tex]\frac{0-\frac{1}{3}}{\frac{2}{3}-\frac{-1}{3}}[/tex].
i.e. Slope = [tex]\frac{0-\frac{1}{3}}{\frac{2}{3}+\frac{1}{3}}[/tex].
i.e. Slope = [tex]\frac{\frac{-1}{3}}{1}[/tex].
Hence, the slope of the line is [tex]\frac{-1}{3}[/tex].
