Question

Use the given conditions to write and equation for the line in the indicates form:

Answer 1

We know that
the equation of the line in slope-intercept form--------------> y=mx+b

Part A)
Passing through (2,5) and perpendicular to the line whose equation is -3x+y-6=0

Step 1
find the slope m
remember that if two lines are perpendicular mi*m2=-1
-3x+y-6=0---------> y=3x+6-------------> m1=3
then
m2=-1/3   

Step 2
find the value of b
point (2,5)  m=-1/3
y=mx+b----------> 5=(-1/3)*2+b--------> b=5+(2/3)-----> b=17/3

Step 3
find the equation of the line in slope-intercept form
y=(-1/3)x+17/3

using a graph tool
see the attached figure

the answer part A) is y=(-1/3)x+17/3

Part B)
Passing through (2,5) and perpendicular to the line whose equation is -3x-6=7x; slope intercept form.

Step 1
-3x-6=7x---------> 10x=-6 -----> x=-6/10-----> x=-3/5 (parallel to the axis y)
equation of the line is a constant so its perpendicular will be another constant defined by the coordinate y of the point through which it passes parallel to the axis x

point (2,5)  ----------> the coordinate y=5
therefore
the perpendicular line is y=5 (parallel to the axis x) 

using a graph tool
see the attached figure

the answer part B) is y=5