Write an equation of the line that passes through the points (-1, 3) and (2, -3).
y = -2x + 1

y = -2x + 5

y = (-½)x + (5/2)

y = (-½)x + (½)

Hello from MrBillDoesMath!

y = -2x + 1

Discussion:

Let m = slope of line. Then

m = (change in y ) / (change in x)

   = (-3 - 3)/(2- -1)

   = -6/ (2 +1)

   = -6/3

   = -2

So y = mx + b = -2x + b. As the line passes through the point (2, -3), by substitution,

-3 =-2(2) + b                   => as 4 to both sides

-3 + 4 = ( -2(2) +4) + b    => (-2(2) +4) = -4 + 4 = 0

1 = 0 + b                          =>

b = 1

The equation of the line is y = -2x + 1, the first choice provided

Thank you,

MrB

m a t h w a y. c o m

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is