Given:
Point (3,3)
The equation of the line,
[tex]y=\frac{3}{5}x+2[/tex]
To find the equation of the line that passes through (3,3) and is perpendicular to the line:
The perpendicular slope is,
[tex]m=-\frac{5}{3}[/tex]
Using the point-slope formula,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{5}{3}(x-3) \\ y=-\frac{5}{3}x+5+3 \\ y=-\frac{5}{3}x+8 \end{gathered}[/tex]
Hence, the equation of the line is,
[tex]y=-\frac{5}{3}x+8[/tex]
Let us find the intercepts.
When x=0, we get y=8
So, the y-intercept is (0,8).
When y=0, we get
[tex]\begin{gathered} -\frac{5}{3}x+8=0 \\ \frac{5}{3}x=8 \\ x=\frac{24}{5} \\ x=4.8 \end{gathered}[/tex]
So, the x-intercept is (4.8,0).
Hence, the correct option which satisfies the equation of the line is D (last option).
