Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through $(2, 7)$ and perpendicular to $3 x + 5 y = 1$ .
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.)

Answer

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Answer

$y = \frac{5}{3} x + \frac{11}{3}$ is the equation in slope-intercept form and $5 x - 3 y = - 11$ is the equation in standard form

Steps

Step 1 ：Convert the given line $3 x + 5 y = 1$ to slope-intercept form: $y = - \frac{3}{5} x + \frac{1}{5}$

Step 2 ：Find the slope of the line perpendicular to the given line: $m = \frac{5}{3}$

Step 3 ：Use the point-slope form of a line with point $(2, 7)$ and slope $\frac{5}{3}$ : $y - 7 = \frac{5}{3} (x - 2)$

Step 4 ：Convert the equation to slope-intercept form: $y = \frac{5}{3} x + \frac{11}{3}$

Step 5 ：Convert the equation to standard form: $5 x - 3 y = - 11$

Step 6 ： $y = \frac{5}{3} x + \frac{11}{3}$ is the equation in slope-intercept form and $5 x - 3 y = - 11$ is the equation in standard form