Solution:

1. Since line $dd$d is perpendicular to line $cc$, the slope of line $dd$ will be the negative reciprocal of the slope of line $cc$c.
   • Slope of $c=-\frac{3}{7}c\; =\; -\backslash frac\{3\}\{7\}$​
   • Slope of $d=\frac{7}{3}d\; =\; \backslash frac\{7\}\{3\}$​
2. We use the point-slope form of the equation $y-y_1=m(x-x_1)y\; –\; y\_1\; =\; m(x\; –\; x\_1)$, where $mm$m is the slope and $(x_1,y_1)=(2,4)(x\_1,\; y\_1)\; =\; (2,\; 4)$.
3. Substitute the values:

   $y-4=\frac{7}{3}(x-2)y\; –\; 4\; =\; \backslash frac\{7\}\{3\}(x\; –\; 2)$
   

4. Distribute $\frac{7}{3}\backslash frac\{7\}\{3\}$:

   $y-4=\frac{7}{3}x-\frac{14}{3}y\; –\; 4\; =\; \backslash frac\{7\}\{3\}x\; –\; \backslash frac\{14\}\{3\}$​

5. Add 4 (or $\frac{12}{3}\backslash frac\{12\}\{3\}$​) to both sides to solve for $yy$y:

   $y=\frac{7}{3}x-\frac{14}{3}+\frac{12}{\mathrm{3<span></span>}}$$y=\frac{7}{3}x-\frac{2}{\mathrm{3<span></span>}}$

Answer:

The equation of line $dd$d in slope-intercept form is:

$y=\frac{7}{3}x-\frac{2}{3}$