13. Which graph matches the linear equation: 6x+y=−4

Question

(1 point)
Responses
(0,2) (1,-1)
(3,0) (0,-2)
(0,-4) (1,-10)
(1,2) (0,-4)

.

Answer 1

To determine which graph matches the linear equation \( 6x + y = -4 \), we can rearrange the equation into slope-intercept form (y = mx + b) or evaluate it at the given points.

First, let's isolate \( y \) in the equation:

\[ y = -6x - 4 \]

Now, we can check the given points to see if they satisfy the equation.

1. For \( (0, 2) \): \[ y = -6(0) - 4 = -4 \quad \text{(not (0, 2))} \]

2. For \( (1, -1) \): \[ y = -6(1) - 4 = -10 \quad \text{(not (1, -1))} \]

3. For \( (3, 0) \): \[ y = -6(3) - 4 = -22 \quad \text{(not (3, 0))} \]

4. For \( (0, -2) \): \[ y = -6(0) - 4 = -4 \quad \text{(not (0, -2))} \]

5. For \( (0, -4) \): \[ y = -6(0) - 4 = -4 \quad \text{(matches)} \]

6. For \( (1, -10) \): \[ y = -6(1) - 4 = -10 \quad \text{(matches)} \]

7. For \( (1, 2) \): \[ y = -6(1) - 4 = -10 \quad \text{(not (1, 2))} \]

After evaluating the points, we see that \( (0, -4) \) and \( (1, -10) \) satisfy the linear equation \( 6x + y = -4 \).

Thus, the graph that matches the equation must include the points \( (0, -4) \) and \( (1, -10) \).

Answer 2

for sure?

Answer 3

Let's confirm by checking if my calculations were accurate and whether the points satisfy the equation \(6x + y = -4\).

We'll evaluate the equation for all given points again:

1. Point (0, 2): \[ 6(0) + 2 = 2 \quad \text{(not -4)} \]

2. Point (1, -1): \[ 6(1) + (-1) = 6 - 1 = 5 \quad \text{(not -4)} \]

3. Point (3, 0): \[ 6(3) + 0 = 18 + 0 = 18 \quad \text{(not -4)} \]

4. Point (0, -2): \[ 6(0) + (-2) = -2 \quad \text{(not -4)} \]

5. Point (0, -4): \[ 6(0) + (-4) = -4 \quad \text{(matches)} \]

6. Point (1, -10): \[ 6(1) + (-10) = 6 - 10 = -4 \quad \text{(matches)} \]

7. Point (1, 2): \[ 6(1) + 2 = 6 + 2 = 8 \quad \text{(not -4)} \]

8. Point (0, -4) again: \[ 6(0) + (-4) = -4 \quad \text{(matches again)} \]

So, the correct points that satisfy the equation \(6x + y = -4\) are (0, -4) and (1, -10).

Thus, I confirm that my previous answer regarding these two points matching the linear equation is accurate. If a graph reflects these points, it would correctly represent the equation \(6x + y = -4\).