The equation for line $c$ can be written as $y=-\frac{3}{7}x+4$. Perpendicular to line $c$ is line $d$, which passes through the point $(2,4)$. What is the equation of line $d$ ?

Write the equation in slope-intercept form. Write the numbers in the equation as simplified prop ringactions, improper fractions, or integers.
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Work it out Not feeling ready yet? These can help:

Step 1 ：The slope of line $c$ is $-\frac{3}{7}$. The slope of a line perpendicular to line $c$ is the negative reciprocal of the slope of line $c$. Therefore, the slope of line $d$ is $-\frac{1}{-\frac{3}{7}}=\frac{7}{3}$.

Step 2 ：We know that line $d$ passes through the point $(2,4)$. We can use the point-slope form of a line to find the equation of line $d$. The point-slope form of a line is $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step 3 ：Substituting the given point and the slope into the point-slope form, we get $y-4=\frac{7}{3}(x-2)$.

Step 4 ：Solving for $y$, we get $y=\frac{7}{3}x-\frac{14}{3}+4=\frac{7}{3}x-\frac{2}{3}$.

Step 5 ：Therefore, the equation of line $d$ is $y=\frac{7}{3}x-\frac{2}{3}$.

Step 6 ：Using python code to simplify the final answer, we get $\boxed{{\displaystyle y=\frac{7}{3}x-\frac{2}{3}}}$