Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through $(1,9)$ and perpendicular to $3 x+7 y=1$ a) The equation of the line in slope-intercept form is (Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.) b) The equation of the line in standard form is (Type your answer in standard form.)

Step 1 ：First, we need to find the slope of the line that is perpendicular to the given line. The slope of a line in standard form, \(Ax + By = C\), is \(-A/B\). So, the slope of the given line is \(-3/7\). The slope of a line perpendicular to this would be the negative reciprocal, which is \(7/3\).

Step 2 ：Next, we use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. Substituting the given point \((1,9)\) and the slope \(7/3\), we can find the equation of the line in slope-intercept form.

Step 3 ：Finally, we can rearrange this equation into standard form.

Step 4 ：\(\boxed{\text{Final Answer:}}\)

Step 5 ：a) The equation of the line in slope-intercept form is \(\boxed{y = \frac{7}{3}x + \frac{20}{3}}\).

Step 6 ：b) The equation of the line in standard form is \(\boxed{7x - 3y = -20}\).