The point (0, 0) is a solution to which of these inequalities?

answer:

y – 5 < 3x – 4

step-by-step explanation:

when you replace a point in an inequality, and that point is a solution of it, the inequality must remain true.

let's replace the (0,0) on each inequality and see where does this happen.

in each inequality, we will replace the x and the y with a 0.

a.   y + 5 < 3x – 4

0 + 5 < 3*0 - 4

5 < 0 - 4

5 < -4

that's not true because a negative number can't be greater than a positive one.

b.   y + 5 < 3x + 4

0 + 5 < 3*0 + 4

5 < 4

false, 5 is greater than 4.

c.   y – 4 < 3x – 5

0 - 4 < 3*0 - 5

-4 < -5

if we multiply by -1 on both sides, we need to change the direction of the inequality

4 > 5

false.

d.   y – 5 < 3x – 4

0 - 5 < 3*0 - 4

-5 < -4

5 > 4

true.

y – 5 < 3x – 4

312312

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)