Thread: Simple Calculus

Find an equation for the line through (4,-1) and perpendicular to the line through (-2,3) and (3,7).

Please provide all steps as im very confused about what to do

Originally Posted by fvaras89

Find an equation for the line through (4,-1) and perpendicular to the line through (-2,3) and (3,7).

Please provide all steps as im very confused about what to do

first of all find the gradient for the points (-2,3) and (3,7).

$\displaystyle m= \frac{y_2-y_1}{x_2-x_1} = \frac{7-3}{3-(-2)} = \frac{4}{5}$

perpendicualr gradient is $\displaystyle \frac{-1}{m} = \frac{-1}{\frac{4}{5}} = \frac{-5}{4}$

So the line $\displaystyle y=mx+c$ for the perpendicular becomes $\displaystyle y=\frac{-5}{4}x+c$

Now use (4,-1) to find c and you will have your answer....

Thank you so much!!

Is it alright to have the final equation as

y+1 = -5/4 (x-4)?

Its ok, depends what form you are asked to provide your answer in.

Your answer is in the form $\displaystyle y-y_1 = m(x-x_1)$ which is fine.

If you need to find the y-intercept which is common you would need to find c as follows

$\displaystyle y=\frac{-5}{4}x+c$

$\displaystyle -1=\frac{-5}{4}\times 4+c$

$\displaystyle -1=-5+c$

$\displaystyle c=4 \Rightarrow y=\frac{-5}{4}x+4$