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 \(3x+5y=38\) into \(y=mx+b\) form. Lets do it!
\(3x+5y=38\)
= \(5y = -3x+38\) (Subtract 3x from both sides)
= \(y= -\frac{3}{5}x+ \frac{38}{5}\) (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 \(\frac{5}{3}\).
Now that we know the slope, we have to find out the rest of the equation using the slope formula, which is:
\(\frac{y-y _{1} }{x- x_{1} }=m\)
Substituting values, we find that:
\(\frac{y-4}{x-6}= \frac{5}{3}\)
By simplifying this equation to slope-intercept form (By cross-multiplying then simplifying), we then get that:
\(y= \frac{5}{3}x-6\) , which is our final answer.
Thank you, and I wish you luck.
