Use a graphing utility to graph the equation below. Then use the TRACE feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. Check the result by using the coefficient of x in the line's equation. $$ y=-2 x-4 $$ Choose the correct aranh below

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UpStudy AI · Accepted Answer

To solve the problem, we will follow these steps:

1. **Graph the equation**: The equation given is $$ y = -2x - 4 $$. This is a linear equation in slope-intercept form, where the slope $$ m $$ is -2 and the y-intercept $$ b $$ is -4.

2. **Identify two points on the line**: We can find two points by substituting different values for $$ x $$ into the equation.

3. **Calculate the slope**: The slope $$ m $$ can be calculated using the formula:
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   where $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ are the coordinates of the two points.

4. **Check the slope using the coefficient of $$ x $$**: The slope can also be confirmed by looking at the coefficient of $$ x $$ in the equation.

Let's start by finding two points on the line. We can choose $$ x = 0 $$ and $$ x = 1 $$:

- For $$ x = 0 $$:
  $$
  y = -2(0) - 4 = -4 \quad \Rightarrow \quad (0, -4)
  $$

- For $$ x = 1 $$:
  $$
  y = -2(1) - 4 = -6 \quad \Rightarrow \quad (1, -6)
  $$

Now we have two points: $$ (0, -4) $$ and $$ (1, -6) $$.

Next, we will calculate the slope using these points:
$$
m = \frac{-6 - (-4)}{1 - 0} = \frac{-6 + 4}{1} = \frac{-2}{1} = -2
$$

Now, we can check the slope using the coefficient of $$ x $$ in the equation $$ y = -2x - 4 $$. The coefficient of $$ x $$ is indeed -2, which confirms our calculation.

Thus, the slope of the line is $$ -2 $$.

If you need to graph the equation using a graphing utility, you can input the equation $$ y = -2x - 4 $$ and use the TRACE feature to find the coordinates of the points we calculated.

In summary:
- The two points are $$ (0, -4) $$ and $$ (1, -6) $$.
- The calculated slope is $$ -2 $$.
- The coefficient of $$ x $$ in the equation confirms the slope as $$ -2 $$.
The slope of the line $$ y = -2x - 4 $$ is $$ -2 $$.

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