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....
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
$\displaystyle y=\frac{-5}{4}x+c$
$\displaystyle -1=\frac{-5}{4}\times 4+c$
$\displaystyle -1=-5+c$
$\displaystyle c=4 \Rightarrow y=\frac{-5}{4}x+4$