Question: which of the following represents the equation of a line that is parallel to the line r shown in the graph?

B

Step-by-step explanation:

• Parallel lines have equal slopes

calculate the slope m of the given line using the gradient formula and compare to the slope of the equations given

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (1,1) ← 2 points on the line

m = = 1 ← slope of graph

consider the slope of the given equations

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

(A)

y = 2x + 1 has slope = 2 → not parallel

(B)

x - y = - 3 ( subtract x from both sides )

- y = - x - 3 ( multiply through by - 1 )

y = x + 3 with slope = 1 → thus parallel to graph

(C)

x + y = 2 ( subtract x from both sides )

y = - x + 2 with slope = - 1 → not parallel

(D)

y = - x + 1 with slope = - 1 → not parallel

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

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5