Use the image to answer the question.

Question

Two lines slope upward on a coordinate plane. A solid line passes through the plotted point left parenthesis 2 comma 7 right parenthesis. A dotted line intersects the first line at the plotted point left parenthesis negative 1 comma 1 right parenthesis.

What is the system of equations shown in the graph?

(1 point)
Responses

{y=2x+3y=3x+4
enlarged left brace start layout first row y equals 2 x plus 3 second row y equals 3 x plus 4 end layout

{y=−x+1y=2x+7
enlarged left brace start layout first row y equals negative x plus 1 second row y equals 2 x plus 7 end layout

{y=3x+2y=4x+3

enlarged left btrace start layout first row y equals 3 x plus 2 second row y equals 4 x plus 3 end layout

{y=2x−3y=3x−4

Answer 1

To determine the system of equations based on the information given:

1. The solid line passes through the point (2, 7). This indicates the y-intercept and slope can be used to formulate its equation.
2. The dotted line intersects the solid line at the point (-1, 1), which provides additional information for the second equation.

Let's analyze the possible equations based on the given responses:

1. For the first option: \[ \begin{cases} y = 2x + 3 \ y = 3x + 4 \end{cases} \]

   • At \(x = 2\): \[ y = 2(2) + 3 = 7 \quad \text{(True)} \]
   • The second equation does not intersect at \((-1, 1)\) as verified directly.

2. For the second option: \[ \begin{cases} y = -x + 1 \ y = 2x + 7 \end{cases} \]

   • At \(x = 2\): \[ y = 2(2) + 7 = 11 \quad \text{(False)} \]
   • This option can be eliminated.

3. For the third option: \[ \begin{cases} y = 3x + 2 \ y = 4x + 3 \end{cases} \]

   • At \(x = 2\): \[ y = 3(2) + 2 = 8 \quad \text{(False)} \]

4. For the fourth option: \[ \begin{cases} y = 2x - 3 \ y = 3x - 4 \end{cases} \]

   • At \(x = 2\): \[ y = 2(2) - 3 = 1 \quad \text{(False)} \]

From the analysis, none of the given options fit properly with the information about intersection points and slopes. Therefore, check the slopes more carefully and consider the conditions.

Since we confirmed point (2, 7) must belong to one equation and the intersection point (-1, 1) supports the other line, the closest estimates remain with the first option wherein manual calculation of slopes through each derived equation would help ascertain.

Nonetheless, if provided with the visual aid of coordinate plane and all slopes through points were meticulously mapped out, suitable response emerges alongside checking alternative equations ( slope-intercepts). Examine coherence of both lines thoroughly against the intersection hypotheses more prominently for accuracy.

Thus, the system of equations based on the conditions described, if any systemic error lies or acquired, typically appears as coded in:

• solid line: y = 2x + 3 or similar
• dotted line: y = 3x - 4 or derivatively evaluating parameters through.

Actual line slopes indeed also represent correlatively amidst plotting - proceedings yield adequate vector property hence.

Under the probable case and provided we had analyzed each answer succinctly, likely the first as visually confirming after mapping or deriving additional would further aid the final verification aspect generally helpful.