I need some help on my algebra 2 homework?

Question

write an equation in point slope form of the line that passes throgh the given points.
1. (6,3) and (-2,1)
2. (-3,-3) and (1,-6)
3. (0,1) and (1,0)
4. Write an equation in standard form of the line that passes through (3,-2) is (a) parallel to (b) perpendicular to y=-2x+3

Answer 1

4)

The point is (3 , -2)

The line equation : y = -2x + 3

The slope of line :m = -2

a)

If two lines are equal then the slopes are equal.

The equation of the point slope form : y - y1 = m(x - x1)

Therefore Substitute m = -2 , x1 = 3 and y1 = -2 in the above equation

y - (-2) = -2(x - 3)

y + 2 = -2x + 6

2x + y  = 4

The standard form of the equation : 2x + y - 4 = 0.

b)

The equation of the line : 2x + y = 3

The perpendicular line equation to the given line  form : x - 2y = k

The point (3 , -2) substitute the above line form 3 - 2(-2) = k

                                                                                      3 + 4 = k

                                                                                        k = 7

                                                                                          x - 2y = 7

The equation standard form : x - 2y - 7 = 0.