The equation of line $c$ is $y=5x-\frac{2}{5}$. Line $d$ is parallel to line $c$ and passes through $(2,6)$. What is the equation of line $d$ ?

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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Step 1 ：The slope of line $d$ is the same as the slope of line $c$ because they are parallel. The slope of line $c$ is $5$. So, the slope of line $d$ is also $5$.

Step 2 ：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 ：We can substitute $(2,6)$ for $(x_1,y_1)$ and $5$ for $m$ to find the equation of line $d$.

Step 4 ：The equation of line $d$ is $5x-y=4$. However, we need to write the equation in slope-intercept form, which is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. We can rearrange the equation to this form.

Step 5 ：The equation of line $d$ in slope-intercept form is $y=5x-4$.

Step 6 ：$\boxed{{\displaystyle y=5x-4}}$