The equation for line f can be written as y=9/5x–2. Perpendicular to line f is line g, which passes through the point (5,–3). What is the equation of line g?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Perpendicular LinesWhen a line is perpendicular, it means that their slope is the negative reciprocal of the reference line.Examples of negative reciprocals:1/3 and -3-4/7 and 7/4Solving the QuestionWe're given:[tex]y=\dfrac{9}{5}x-2[/tex]Passes through (5,–3)Slope intercept form: [tex]y=mx+b[/tex] m = slopeb = y-interceptFinding the slopeWe know that the slope of the line will be the negative reciprocal of [tex]\dfrac{9}{5}[/tex]: [tex]-\dfrac{5}{9}[/tex]⇒ Plug this into y=mx+b:[tex]y=-\dfrac{5}{9}x+b[/tex]Finding the y-interceptTo find the y-intercept, plug in the given point and solve for b:[tex]-3=-\dfrac{5}{9}*5+b\\\\-3=-\dfrac{25}{9}+b\\\\b=-\dfrac{2}{9}[/tex]⇒ Plug this into our equation:[tex]y=-\dfrac{5}{9}x-\dfrac{2}{9}[/tex]Answer[tex]y=-\dfrac{5}{9}x-\dfrac{2}{9}[/tex]

Answer:y = -5/9x -2/9Step-by-step explanation: