The line whose slope is 4 and intersects the line 2x - 4y = 8 at x = 6 has the equation: a. y = 4x + 6 b. y = 4x + 1 c. y = 4x - 23

2x - 4y = 8   →   -4y = -2x + 8   →   y = - 2

We know the slope (m) = 4, need to find y-intercept (b)

y = 4x + b

- 2 = 4x + b

- 2 = 4(6) + b

3 - 2  = 24 + b

1 = 24 + b

-23 = b

Equation: y = 4x - 23

C

true

explanation:

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