Question: Write the English sentence as an equation in two variables. Then graph the equation. The y-value is two more than three times the x-value. Part 1 of 2 Choose the equation that corresponds to the sentence above. A. y equals negative 3 x minus 2 B. y equals negative 3 x plus 2 C. y equals 3 x minus 2 D. y equals 3 x plus 2 Part 2 of 2 Choose the graph of the equation above. A. A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line rises from left to right and passes through the points (0, negative 2) and (1, 1). -8 -4 4 8 -8 -4 4 8 x y A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line rises from left to right and passes through the points (0, negative 2) and (1, 1). B. A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line rises from left to right and passes through the points (0, 2) and (1, 5). -8 -4 4 8 -8 -4 4 8 x y A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line rises from left to right and passes through the points (0, 2) and (1, 5). C. A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line falls from left to right and passes through the points (0, 2) and (1, negative 1). -8 -4 4 8 -8 -4 4 8 x y A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line falls from left to right and passes through the points (0, 2) and (1, negative 1). D. A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line falls from left to right and passes through the points (0, negative 2) and (1, negative 5). -8 -4 4 8 -8 -4 4 8 x y A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 1 and a vertical y-axis labeled from negative 8 to 8 in increments of 1. A line falls from left to right and passes through the points (0, negative 2) and (1, negative 5).

1. **State the problem:** We are given the sentence: "The y-value is two more than three times the x-value." We need to write this as an equation in two variables $x$ and $y$, then identify the correct graph. 2. **Translate the sentence into an equation:** "Two more than three times the x-value" means: $$y = 3x + 2$$ This is because "three times the x-value" is $3x$, and "two more than" means add $2$. 3. **Check the options for the equation:** - Option A: $y = -3x - 2$ (incorrect sign for slope and intercept) - Option B: $y = -3x + 2$ (incorrect slope sign) - Option C: $y = 3x - 2$ (incorrect intercept) - Option D: $y = 3x + 2$ (correct) So, the correct equation is **D**. 4. **Analyze the graph options:** The equation $y = 3x + 2$ has: - y-intercept at $(0, 2)$ - slope $3$, meaning for each increase of $1$ in $x$, $y$ increases by $3$. Check the points given in the graphs: - Graph A: passes through $(0, -2)$ and $(1, 1)$ (incorrect intercept) - Graph B: passes through $(0, 2)$ and $(1, 5)$ (correct: $5 = 3(1) + 2$) - Graph C: passes through $(0, 2)$ and $(1, -1)$ (incorrect slope) - Graph D: passes through $(0, -2)$ and $(1, -5)$ (incorrect intercept and slope) Therefore, the correct graph is **B**. **Final answers:** - Equation: $$y = 3x + 2$$ (Option D) - Graph: Option B