Iwill give ! lots of !

which system of inequalities is represented by the graph?

a) y ≤ x - 5 and y ≥ -3x + 2

b) y ≤ x - 5 and y ≥ -3x - 2

c) y ≤ -x + 5 and y ≥ 3x - 2

d) y ≤ x + 5 and y ≥ -3x - 2

Option B) y ≤ x - 5 and y ≥ -3x - 2

Step-by-step explanation:

step 1

Find the equation of the inequality with y-intercept -5

The equation of the solid line has a positive slope

Take the ordered pairs (0,-5) and (4,-1) to find the slope

The equation of the solid line is

The solution of the inequality is the shaded area below the solid line

therefore

The equation of the first inequality is

step 2

Find the equation of the inequality with y-intercept -2

The equation of the solid line has a negative slope

Take the ordered pairs (0,-2) and (1,-5) to find the slope

The equation of the solid line is

The solution of the inequality is the shaded area above (to the right) the solid line

therefore

The equation of the second inequality is

step 3

The system of inequalities is

can you complete your sentence? i could !

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b