find an equation of the line satisfying the given conditionsthrough (6,4); perpendicular to 3x + 5y =38

To answer this, we will need to know:

• The slope of the equation we are trying to get
• The point it passes through using the 

First, we will need to find the slope of this equation. To find this, we must simplify the equation  into  form. Lets do it!


=  (Subtract 3x from both sides)
=  (Divide both sides by 5) 

The slope of a line perpendicular would have to multiply with the equation we just changed to equal -1. In other words, it would have to equal the negative reciprocal.

The negative reciprocal of the line given is . 

Now that we know the slope, we have to find out the rest of the equation using the slope formula, which is:



Substituting values, we find that:



By simplifying this equation to slope-intercept form (By cross-multiplying then simplifying), we then get that: 

, which is our final answer.

Thank you, and I wish you luck.