Question

Write an equation in point-slope form of the line that passes through the given points:
1. (5,-6), (1,-7)
2. (6,-3), (-1,9)

3. write an equation of a line that is perpendicular to y=-3x+5 and passes through (4,3).

Answer 1

for #1 and #2
first find the slope, that gives you the m.
Now pick one of the given points and sub those values into
y = mx + b
Solve for b and rewrite the equation.

I am sure that your teacher and/or your textbook has given you several examples of this type of fundamental question.

#3.
The line perpedicular to the given line must have slope of 1/3

so new equation:
y = (1/3)x + b
sub in (4,3)
3 = (1/3)(4) + b
I usually get rid of my fractions by multiplying by whatever the denominator is
9 = 4 + 3b
b = 5/3

final equation : y = (1/3)x + 5/3