Question

What is the equation of the line that is perpendicular to the line 5x – 3y = 2 and passes through the point (-1,3)?

Answer 1

3x+5y=12.

Step-by-step explanation:

Given the line: 5x-3y=2

First, we determine the slope by making y the subject of the equation.

`\begin{gathered} 3y=5x-2 \\ y=(5)/(3)x-(2)/(3) \end{gathered}`

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:

`\begin{gathered} (5)/(3)* n=-1 \\ n=-(3)/(5) \end{gathered}`

Next, we use the point-slope form to find the perpendicular to the given line that is passing through (-1, 3).

`\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-(3)/(5)(x-(-1)) \\ y-3=-(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}`

The required equation is 3x+5y=12.