What is the equation of the line that passes through the point (4,−2) and has a slope of
−2?

Point-slope form:

y

−

2

=

−

3

x

+

12

Slope-intercept form:

y

=

−

3

x

+

14

Explanation:

First write a point-slope equation

y

−

y

1

=

m

(

x

−

x

1

)

, where

(

x

1

,

y

1

)

is the given point,

(

4

,

2

)

, and

m

is the slope,

−

3

.

y

−

2

=

−

3

(

x

−

4

)

y

−

2

=

−

3

x

+

12

For graphing, you can convert to the slope-intercept form,

y

=

m

x

+

b

, by solving for

y

, where

m

is the slope and

b

is the y-intercept.

Add

2

to both sides.

y

=

−

3

x

+

12

+

2

y

=

−

3

x

+

14

m

=

−

3

and

b

=

14

graph{y=-3x+14 [-10.72, 9.29, 7.66, 17.66]}

power property.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.