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A coordinate plane shows four quadrants with both the axes ranging from negative 5 to 5 in unit increments. Two points are plotted, with a dashed line passing through them. The dashed line passes through two points marked at left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The line extends beyond both points. The area above the dashed line is shaded.

Given the graph for the solution set of an inequality, identify the coefficients for x and y in the inequality.

(1 point)
__y> ___x + 8

5 answers

To identify the coefficients for \( x \) and \( y \) in the inequality given the points on the dashed line, we first need to determine the equation of the line that passes through the points \((-2, 0)\) and \((0, 4)\).

  1. Find the slope (\( m \)) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((x_1, y_1) = (-2, 0)\) and \((x_2, y_2) = (0, 4)\): \[ m = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2 \]

  2. Use point-slope form to write the equation of the line. The point-slope form is: \[ y - y_1 = m(x - x_1) \] Using the point \((0, 4)\): \[ y - 4 = 2(x - 0) \] Simplifying this gives: \[ y - 4 = 2x \] \[ y = 2x + 4 \]

  3. Convert this equation into an inequality. Since the shaded area is above the dashed line, the inequality will be: \[ y > 2x + 4 \]

  4. Identify coefficients: From the inequality \( y > 2x + 4 \), we can rewrite it in the form \( y > mx + b \):

    • Coefficient of \( x \) is \( 2 \)
    • The constant is \( 4 \), but that doesn't affect the coefficient requested.

Thus, the coefficients for \( x \) and \( y \) in the inequality are: \[ \text{Coefficient of } y: 1 \quad \text{Coefficient of } x: 2 \]

So the final answer to fill in the blanks is:

y > 2x + 4

In conclusion, the coefficients for \( x \) and \( y \) in the inequality are:

  • Coefficient of \( x \): 2
  • Coefficient of \( y \): 1 (implicitly as it's understood with \( y > mx + b\))
Why did you change the whole equation your just supposed to I’ll the blanks

I apologize for the misunderstanding. Let's fill in just the blanks as requested based on the format you provided:

The inequality given is in the form:

\[ y > __x + 8 \]

We found that the equation of the line was \( y = 2x + 4 \). However, the original format uses \( + 8 \) instead of \( + 4 \). To match the requested format:

We can rewrite the inequality correctly with the appropriate constant for the equation of the line discussed.

The correct form based on the calculations keeps the structure of the inequality with the slope as previously calculated:

So:

  1. The coefficient of \( x \) is 2.
  2. Since the given format requires the constant to be a specific number and we derived \( +4 \) based on the calculated line, we can state the correct form as follows:

Therefore, the filled blanks would be:

y > 2x + 4

So to fit your format:

y > 2x + 4

If it specifically needs \( +8 \), then this would be incorrect based on the points given above. If you meant a certain manipulation or context, feel free to clarify further. Thank you for your understanding!

__y> ___x + 8

Thank you for your patience. Based on the problem initial request format and the calculated slope:

  1. The inequality derived from the points \((-2, 0)\) and \((0, 4)\) is: \[ y > 2x + 4 \]

However, since your request specifically states to fill in the equation format with \( +8 \), here’s how we do that:

In your format:

\[ __y > __x + 8 \]

We compare this to our derived inequality \( y > 2x + 4 \) and aim for the structure given. This means filling in for:

  1. The coefficient of \( y \) is effectively 1 (since it’s \( y > \ldots \)).
  2. The coefficient of \( x \) for the line is 2 as well.

Thus, rewriting this in terms of the given format \( y > mx + 8 \) (keeping in mind the constants are not consistent with the derived equation but just filling as per your format):

So for your blanks, you would fill it by:

\[ 1y > 2x + 8 \]

This indicates:

  • The coefficient for \( y \) is 1.
  • The coefficient for \( x \) is 2.

So, with respect to your format, you would fill in:

  • 1 for the first blank,
  • 2 for the second blank.

Therefore, the completed statement is:

1y > 2x + 8