Math / Algebra

Question7 The graph of $-3 x+5 y=-15$ is shown. Which points are in the solution set of (Select two correct answers.) $-3 x+5 y \geq-15$
A $(-1,-7)$ B $(1,-3)$ C $(6,-1)$ D $(0,-3)$ E $(0,0)$

Studdy Solution

STEP 1

What is this asking? Which of the given points make the inequality $-3x + 5y \geq -15$ true? Watch out! Remember, the line itself is part of the solution set because the inequality includes "greater than or equal to".

STEP 2

1. Test each point
2. Interpret the results

STEP 3

Let's plug in $(-1, -7)$ into our inequality $-3x + 5y \geq -15$ .
We substitute $x = -1$ and $y = -7$ : $-3 \cdot (-1) + 5 \cdot (-7) \geq -15$ $3 - 35 \geq -15$ $-32 \geq -15$ This is false! $-32$ is less than $-15$ .

STEP 4

Now let's test point B $(1, -3)$ .
We substitute $x = 1$ and $y = -3$ : $-3 \cdot (1) + 5 \cdot (-3) \geq -15$ $-3 - 15 \geq -15$ $-18 \geq -15$ This is also false! $-18$ is less than $-15$ .

STEP 5

Let's try point C $(6, -1)$ .
We substitute $x = 6$ and $y = -1$ : $-3 \cdot (6) + 5 \cdot (-1) \geq -15$ $-18 - 5 \geq -15$ $-23 \geq -15$ Nope, still false! $-23$ is less than $-15$ .

STEP 6

Time for point D $(0, -3)$ .
We substitute $x = 0$ and $y = -3$ : $-3 \cdot (0) + 5 \cdot (-3) \geq -15$ $0 - 15 \geq -15$ $-15 \geq -15$ Yes! This is true! $-15$ is equal to $-15$ .

STEP 7

Finally, let's check point E $(0, 0)$ .
We substitute $x = 0$ and $y = 0$ : $-3 \cdot (0) + 5 \cdot (0) \geq -15$ $0 + 0 \geq -15$ $0 \geq -15$ This is true! $0$ is greater than $-15$ .

STEP 8

The correct answers are D and E.

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Question7 The graph of $-3 x+5 y=-15$ is shown. Which points are in the solution set of (Select two correct answers.) $-3 x+5 y \geq-15$
A $(-1,-7)$ B $(1,-3)$ C $(6,-1)$ D $(0,-3)$ E $(0,0)$

Studdy Solution

STEP 1

What is this asking? Which of the given points make the inequality $-3x + 5y \geq -15$ true? Watch out! Remember, the line itself is part of the solution set because the inequality includes "greater than or equal to".

STEP 2

1. Test each point
2. Interpret the results

STEP 3

Let's plug in $(-1, -7)$ into our inequality $-3x + 5y \geq -15$ .
We substitute $x = -1$ and $y = -7$ : $-3 \cdot (-1) + 5 \cdot (-7) \geq -15$ $3 - 35 \geq -15$ $-32 \geq -15$ This is false! $-32$ is less than $-15$ .

STEP 4

Now let's test point B $(1, -3)$ .
We substitute $x = 1$ and $y = -3$ : $-3 \cdot (1) + 5 \cdot (-3) \geq -15$ $-3 - 15 \geq -15$ $-18 \geq -15$ This is also false! $-18$ is less than $-15$ .

STEP 5

Let's try point C $(6, -1)$ .
We substitute $x = 6$ and $y = -1$ : $-3 \cdot (6) + 5 \cdot (-1) \geq -15$ $-18 - 5 \geq -15$ $-23 \geq -15$ Nope, still false! $-23$ is less than $-15$ .

STEP 6

Time for point D $(0, -3)$ .
We substitute $x = 0$ and $y = -3$ : $-3 \cdot (0) + 5 \cdot (-3) \geq -15$ $0 - 15 \geq -15$ $-15 \geq -15$ Yes! This is true! $-15$ is equal to $-15$ .

STEP 7

Finally, let's check point E $(0, 0)$ .
We substitute $x = 0$ and $y = 0$ : $-3 \cdot (0) + 5 \cdot (0) \geq -15$ $0 + 0 \geq -15$ $0 \geq -15$ This is true! $0$ is greater than $-15$ .

STEP 8

The correct answers are D and E.

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Studdy Solution

STEP 1

What is this asking? Which of the given points make the inequality −3x+5y≥−15-3x + 5y \geq -15−3x+5y≥−15 true? Watch out! Remember, the line itself is part of the solution set because the inequality includes "greater than *or equal to*".

STEP 2

1. Test each point2. Interpret the results

STEP 3

STEP 4

STEP 5

STEP 6

STEP 7

STEP 8

The correct answers are D and E.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Which of the given points make the inequality $-3x + 5y \geq -15$ true? Watch out! Remember, the line itself is part of the solution set because the inequality includes "greater than or equal to".

1. Test each point
2. Interpret the results