Write an equation in slope-intercept form of the line with the given characteristics:

1. Slope: -3; passes through (0,5),

2. Passes through (0, -2) and (4,-1)

1. y = -3x + 5

2. y = 1/4x - 2

Step-by-step explanation:

y=mx+b

1. 5 = -3(0) + b, so b = 5

y = -3x + 5

2. (-2-(-1))/(0-4) = -1/-4 = 1/4

-2 = 1/4(0) + b, so b = -2

y = 1/4x - 2

it would open into a square depending on the type of envelope i’m not sure about the second part

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true