Respuesta :
Answer:
3x+5y=12.
Explanation:
Given the line: 5x-3y=2
First, we determine the slope by making y the subject of the equation.
[tex]\begin{gathered} 3y=5x-2 \\ y=\frac{5}{3}x-\frac{2}{3} \end{gathered}[/tex]Comparing with the slope-intercept form: y=mx+b
• Slope = 5/3
Let the slope of the perpendicular line = n
By definition. two lines are perpendicular if the product of their slopes is -1.
Therefore:
[tex]\begin{gathered} \frac{5}{3}\times n=-1 \\ n=-\frac{3}{5} \end{gathered}[/tex]Next, we use the point-slope form to find the perpendicular to the given line that is passing through (-1, 3).
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{3}{5}(x-(-1)) \\ y-3=-\frac{3}{5}(x+1)\text{ Multiply both sides by 5} \\ 5(y-3)=-3(x+1) \\ 5y-15=-3x-3 \\ 5y+3x=-3+15 \\ 3x+5y=12 \end{gathered}[/tex]The required equation is 3x+5y=12.
