Problem

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.)

Solution

Step 1 :Convert the given line $3x + 5y = 1$ 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: $5x - 3y = -11$

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

From Solvely APP
Source: https://solvelyapp.com/problems/22574/

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