Question

Determine if the ordered pair (−1, −5) is a solution to the inequality y is less than or equal to negative three fourths times x minus 1. No, because (−1, −5) is above the line Yes, because (−1, −5) is below the line No, because (−1, −5) is on the line Yes, because (−1, −5) is on the line

Answer 1

the answer is [yes, because (-1, -5) is below the solid line].

Explanation:

I took the test and got it right

Answer 2

Yes, because (−1, −5) is below the line.

Step-by-step explanation:

The given inequality is
`y \leq  -(3)/(4) x - 1` .......... (1)

Now, rearranging this equality relation we get,

4y = - 3x - 4

⇒ 3x + 4y = - 4

⇒
`(x)/(- (4)/(3) ) + (y)/(- 1) = 1` .......... (2)

This equation is in intercept form and the line represented by this equation passes through the x-intercept
`(- (4)/(3), 0)` and y-intercept (0,-1).

Now, it is clear that (0,0) point is above the equation.

But (0,0) point does not satisfy the inequality equation (1).

Hence, the solution of the inequality equation (1) is below and including line (2).

Now, point (-1,-5) is below the line (2) and hence, it is a solution of the inequality (1) as it is below the line. (Answer)