Which of the following graphs represents the equation y - 4 = 3(x - 1)?A.Graph AB.Graph BC.Graph CD.Graph DSUBMITarrow_backPREVIOUS

To determine which graph represents the equation $y - 4 = 3(x - 1)$, we first need to rewrite the equation in slope-intercept form ( $y = mx + b$ ).

1. Break Down the Problem

We will solve for $y$ to identify the slope and the y-intercept, as these are essential for graphing the equation.

2. Relevant Concepts

Starting from: $y - 4 = 3(x - 1)$

We can use algebra to rearrange this into slope-intercept form.

3. Analysis and Detail

Step 1: Distribute the 3 on the right side. $y - 4 = 3x - 3$

Step 2: Add 4 to both sides to isolate $y$. $y = 3x - 3 + 4$ $y = 3x + 1$

In this form, we see that the slope $m = 3$ and the y-intercept $b = 1$ (the point where the line crosses the y-axis).

4. Verify and Summarize

We've determined the equation in slope-intercept form is $y = 3x + 1$, indicating that the line has a slope of 3 (rising 3 units for every 1 unit it moves to the right) and crosses the y-axis at $1$.

Final Answer

Look for the graph among the choices that has a y-intercept of $1$ and a slope of $3$ (which is a relatively steep slope). Based on this analysis, select the graph that matches these features.