Use the image to answer the question.

Question

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

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

GPT-4o mini · Answer

To find the coefficients for $x$ and $y$ in the given inequality $y > x + 8$ based on the graph described, we can analyze the points that the dashed line passes through. The two points marked on the dashed line are $(-2, 0)$ and $(0, 4)$. 1. **Calculate the slope of the line**: The slope $m$ is calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Where $(x_1, y_1) = (-2, 0)$ and $(x_2, y_2) = (0, 4)$: $$ m = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2 $$ 2. **Use point-slope form to find the equation of the line**: Using the point-slope form $y - y_1 = m(x - x_1)$: $$ y - 0 = 2(x + 2) $$ This simplifies to: $$ y = 2x + 4 $$ 3. **Rearranging the equation**: We can express this in the standard linear form: $$ 2x - y + 4 = 0 $$ Rearranging gives: $$ -y = -2x - 4 $$ Flipping the signs: $$ y = 2x + 4 $$ 4. **Identifying the inequality**: Since the area above the dashed line is shaded, the inequality is: $$ y > 2x + 4 $$ Thus, the coefficients for $x$ and $y$ in the inequality are: - Coefficient of $x$ is $2$ - Coefficient of $y$ is $-1$ (since it is $y - 2x - 4 > 0$) Therefore, the complete answer is: **Coefficients for $x$ and $y$ in the inequality:** $y > 2x + 4$.

Answer

no

GPT-4o mini · Answer

I apologize for any confusion. Let's start over and address the problem more clearly.

Based on your description, it seems the dashed line passes through the coordinates $(-2, 0)$ and $(0, 4)$.

Equation of the Line: We first find the slope between the two points: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2. \]

Now we use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1). \] Using point $(0, 4)$: \[ y - 4 = 2(x - 0) \implies y = 2x + 4. \]
Rearranging the Equation: The equation in standard form is: \[ -2x + y - 4 = 0 \implies 2x - y + 4 = 0 \implies y = 2x + 4. \]
Setting Up the Inequality: Since the area above the dashed line is shaded, we denote this as: \[ y > 2x + 4. \]

Based on the standard form of the line $y = mx + b$, where $m$ is the coefficient of $x$, we find:

Coefficient of $x$ is $2$,
Coefficient of $y$ when rearranged to the form $Ax + By > C$ is $-1$ (which comes from the rearranged equation $2x - y + 4 > 0$).

So the inequality can be rewritten to show coefficients explicitly:

Answer:

The coefficients in the inequality $y > 2x + 4$ are:

Coefficient of $x$: $2$,
Coefficient of $y$: $-1$.

If there are further specifics to clarify or adjust about my response or if you have another question, please let me know!