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Which equation best represents the relationship between x
 and y
 in the graph?
A.y=3x+3

B.y=3x−1

C.y=13x+3


The graph you provided represents a straight line, which can be described by the equation of the form \( y = mx + b \), where:
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \)).

### Step 1: Find the slope \( m \)
The slope \( m \) is calculated as:
\[
m = \frac{\text{change in } y}{\text{change in } x}
\]
From the graph, the line passes through points \( (1, 3) \) and \( (2, 6) \).

So, the slope is:
\[
m = \frac{6 - 3}{2 - 1} = \frac{3}{1} = 3
\]

### Step 2: Find the y-intercept \( b \)
Looking at the graph, the line intersects the y-axis at \( y = 0 \), so the y-intercept \( b = -1 \).

### Step 3: Equation of the line
Using \( m = 3 \) and \( b = -1 \), the equation of the line is:
\[
y = 3x - 1
\]

Therefore, the correct equation is:

**B. \( y = 3x - 1 \)**.

Would you like more details or have any questions?

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Here are five related questions for further exploration:
1. How do you find the slope of a line given two points?
2. What does the y-intercept represent in a graph?
3. How can you graph a linear equation if you know its slope and y-intercept?
4. How does changing the slope affect the steepness of the line?
5. How does the y-intercept shift the graph vertically?

**Tip**: To verify an equation of a line, you can substitute points from the graph into the equation to see if they satisfy it.

Which equation best represents the relationship between x and y in the graph? A. y = 3x + 3 B. y = 3x - 1 C. y = 13x + 3

Solve the linear equation problem by determining the slope and y-intercept from the graph. Learn how to calculate the slope using two points and apply the equation y = mx + b. Suitable for Grades 7-9.

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