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Which of the following points is a solution to the linear inequality y>1/9x−2/9 ?(1 point)

Responses

(0,−4/9)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis

(0,−1/9)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis

(0,−2/9)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis

(0,−1/3)

5 answers

To determine which of the given points is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute the \( x \) and \( y \) values from each point into the inequality and see if it holds true.

  1. Point (0, -4/9): \[ y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow -\frac{4}{9} > -\frac{2}{9} \quad \text{(False)} \]

  2. Point (0, -1/9): \[ y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow -\frac{1}{9} > -\frac{2}{9} \quad \text{(True)} \]

  3. Point (0, -2/9): \[ y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow -\frac{2}{9} > -\frac{2}{9} \quad \text{(False)} \]

  4. Point (0, -1/3): \[ y > \frac{1}{9}(0) - \frac{2}{9} \Rightarrow -\frac{1}{3} > -\frac{2}{9} \quad \text{(False)} \]

The only point that satisfies the inequality is (0, -1/9).

So the final answer is: (0, -1/9).

Show which of the following points is part of the solution set for the inequality y≤2/5x+1.(1 point)
Responses

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

(10,6)
left parenthesis 10 comma 6 right parenthesis

(10,4)
left parenthesis 10 comma 4 right parenthesis

(−10,6)

To determine which of the given points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we substitute the \( x \) and \( y \) values from each point into the inequality and verify whether it holds true.

  1. Point (10, 5.5): \[ y \leq \frac{2}{5}(10) + 1 \ 5.5 \leq 4 + 1 \ 5.5 \leq 5 \quad \text{(False)} \]

  2. Point (10, 6): \[ y \leq \frac{2}{5}(10) + 1 \ 6 \leq 4 + 1 \ 6 \leq 5 \quad \text{(False)} \]

  3. Point (10, 4): \[ y \leq \frac{2}{5}(10) + 1 \ 4 \leq 4 + 1 \ 4 \leq 5 \quad \text{(True)} \]

  4. Point (−10, 6): \[ y \leq \frac{2}{5}(-10) + 1 \ 6 \leq -4 + 1 \ 6 \leq -3 \quad \text{(False)} \]

The point that satisfies the inequality \( y \leq \frac{2}{5}x + 1 \) is (10, 4).

So the final answer is: (10, 4).

Write a two-variable linear inequality that models the graph of the solid line y=2x−4 with a shaded region above the line. Which of the following options is correct?(1 point)
Responses

y≥2x−4
y greater-than-or-equal-to 2 x minus 4

y>2x−4
y greater than 2 x minus 4

y≤2x−4
y less-than-or-equal-to 2 x minus 4

y<2x−4

To model the graph of the solid line \( y = 2x - 4 \) with a shaded region above the line, we need to choose the correct type of inequality.

  • A solid line indicates that the points on the line itself are included in the solution set, so we will use either \(\geq\) or \(\leq\).
  • Since the shaded region is above the line, we want to represent all of the points above the line, which would require a "greater than or equal to" inequality.

Thus, the correct inequality to represent the shaded region above the line \( y = 2x - 4 \) with the solid line is:

\[ y \geq 2x - 4 \]

So, the correct response is: y ≥ 2x - 4.