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

1. (6,3) and (-2,1)

Given points are A =(6,3) ; B = (-2,1)

A = (6,3) = (x1,y1) and B = (-2,1) =(x2,y2) say

Slope m = y2-y1 / x2-x1

Slope m = 1-3 / -2-6

Slope m = -2 / -8

Slope m = 2/8

Slope m =1/4

Answer 2

2. (-3,-3) and (1,-6)

Given points are A =(-3,-3) ; B = (1,-6)

A = (-3,-3) = (x1,y1) and B = (1,-6) =(x2,y2) say

Slope m = y2-y1 / x2-x1

Slope m = -6-(-3) / 1-(-3)

Slope m = -6+3 / 1+3

Slope m = -3/ 4

 

 

Answer 3

3. (0,1) and (1,0)

Given points are A =(0,1) ; B = (1,0)

A = (0,1) = (x1,y1)  and  B  = (1,0) = (x2,y2)  say

Slope m = y2-y1 / x2-x1

Slope m = 0-1 / 1-0

Slope m = -1 / 1

Slope m = -1

 

Answer 4

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

Given point (3,-2) and equation y = - 2x+3

(a) y = 2x+3 paraiiei line equation y =  -2x+k -------------(1)

And equation(1) passes point (3,-2)

-2 = 2(3)+k

-2 = 6+k

Substrct 6 from each side

-2-6 = -6+6+k

-8 = k

k = -8 subsute in equation (1)

y = -2x -8

paraiiei line equation y +2x+8 =0

(b) perpendicular to y=-2x+3

Given slope m = -2

perpendicular slope =  -1 / m

                            =  -1 / -2

perpendicular slope =1/2

perpendicular line eqation y = (1/2)x+3

Multiply each side by 2

perpendicular line equation 2y = x+6

perpendicular line equation 2y-x-6 = 0

                         

Answer 5

Given points are A =(6,3) ; B = (-2,1)

A = (6,3) = (x1,y1) and B = (-2,1) =(x2,y2) say

Slope m = y2-y1 / x2-x1

Slope m = 1-3 / -2-6

Slope m = -2 / -8

Slope m = 2/8

Slope m =1/4

The equation in point slope form is : y - y1 = m ( x - x1)

y - 3 = (1/4) ( x - 6 )

Cross multiplication

4 (y - 3) = x - 6

4y - 12 = x - 6

Subtract 4y - 12 from each side

0 = x - 6 - 4y + 12

0 = x - 4y + 6

i.e x - 4y + 6 = 0

The equation in point slope form passing through two points is x - 4y +6 =0

Answer 6

 

2. (-3,-3) and (1,-6)

Given points are A =(-3,-3) ; B = (1,-6)

A = (-3,-3) = (x1,y1) and B = (1,-6) =(x2,y2) say

Slope m = y2-y1 / x2-x1

Slope m = -6-(-3) / 1-(-3)

Slope m = -6+3 / 1+3

Slope m = -3/ 4

The equation in point slope form is y - y1 = m (x - x1)

y - (-3) = -3/4 (x -(-3))

The product of two same signs is positive

y + 3 = -3/4 (x + 3)

Cross multiplication

4 (y +3) = -3 ( x +3)

Distribute terms using distributive property : a (b + c) = ab + ac

4y + 12 = -3(x) - 3(+3)

The product of two different signs is negative

4y + 12 = - 3x - 9

Subtract - 3x -9 from each side

4y + 12 - ( -3x -9) = -3x - 9 - (-3x - 9)

4y + 12 + 3x + 9 = 0

i.e , 3x + 4y + 21 =0

The equation in point slope form passing through two points is 3x + 4y + 21 =0

Answer 7

 

3. (0,1) and (1,0)

Given points are A =(0,1) ; B = (1,0)

A = (0,1) = (x1,y1)  and  B  = (1,0) = (x2,y2)  say

Slope m = y2-y1 / x2-x1

Slope m = 0-1 / 1-0

Slope m = -1 / 1

Slope m = -1

The equation in point slope form is y - y1 = m (x - x1)

y - 1 = -1 (x - 0)

y - 1 = -1 (x)

y - 1 = - x

Add x to each side

y - 1 + x = - x + x

i.e, x + y - 1 = 0

The equation of line in point slope form passing through two points is x + y - 1 = 0 

Answer 8

1. (6,3) and (-2,1)

Given points are A =(6,3) ; B = (-2,1)

A = (6,3) = (x1,y1) and B = (-2,1) =(x2,y2) say

Slope m = y2-y1 / x2-x1

Slope m = 1-3 / -2-6

Slope m = -2 / -8

Slope m = 2/8

Slope m =1/4

Equation of a line point -slope form y - y1 = m(x - x1)

Substitute m = 1 / 4 , x1 = 6 and y1 = 3 in the above line

y - 3 = 1 / 4(x - 6)

4y - 12 = x - 6

Add 12 to each side

4y = x + 6

The equation of the line : x - 4y + 6 = 0

 

Answer 9

2. (-3,-3) and (1,-6)

Given points are A =(-3,-3) ; B = (1,-6)

A = (-3,-3) = (x1,y1) and B = (1,-6) =(x2,y2) say

Slope m = y2-y1 / x2-x1

Slope m = -6-(-3) / 1-(-3)

Slope m = -6+3 / 1+3

slope m = -3 / 4

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

Substitute m = -3 / 4 , x1 = -3 and y1 = -3 in the above line

y - (-3) = - 3 / 4(x - (-3))

y + 3 = - 3 / 4(x + 3)

4y + 12 = -3x - 9

3x + 4y + 21 = 0.

 

Answer 10

3. (0,1) and (1,0)

Given points are A =(0,1) ; B = (1,0)

A = (0,1) = (x1,y1)  and  B  = (1,0) = (x2,y2)  say

Slope m = y2-y1 / x2-x1

Slope m = 0-1 / 1-0

Slope m = -1 / 1

slope m = -1

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

Substitute m = -1 , x1 = 0 and y1 = 1 in the above line

y - 1 = -1(x - 0)

y - 1 = -x

Add x to each side

y - 1 + x = 0

Add 1 to each side

x + y = 1.