From the image, we need to find the slope (m), y-intercept (b), and the equation of the line shown in the graph.

Step 1: Identifying two points on the line

From the graph, we can identify two points that the line passes through:

• Point 1: $(2, 3)$
• Point 2: $(6, 5)$

Step 2: Calculating the slope ($m$)

The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values: $m = \frac{5 - 3}{6 - 2} = \frac{2}{4} = \frac{1}{2}$

So, the slope is: $m = \frac{1}{2}$

Step 3: Determining the y-intercept ($b$)

The equation of a line in slope-intercept form is: $y = mx + b$ Using one of the points, such as $(2, 3)$, substitute $x = 2$, $y = 3$, and $m = \frac{1}{2}$ into the equation: $3 = \frac{1}{2}(2) + b$ $3 = 1 + b$ $b = 3 - 1 = 2$

So, the y-intercept is: $b = 2$

Step 4: Writing the equation of the line

Using the slope ($m = \frac{1}{2}$) and y-intercept ($b = 2$), the equation of the line is: $y = \frac{1}{2}x + 2$

Final Answer:

• $m = \frac{1}{2}$
• $b = 2$
• Equation: $y = \frac{1}{2}x + 2$

Do you want a more detailed explanation or have any questions?

Here are 5 related questions you can explore:

1. How do you find the slope if the graph is not perfectly aligned with grid points?
2. Can you explain how to convert slope-intercept form ($y = mx + b$) to standard form ($Ax + By = C$)?
3. How do you find the slope of a horizontal or vertical line?
4. What happens to the graph if you increase the slope ($m$) or change the y-intercept ($b$)?
5. How would the equation change if the line had a negative slope?

Tip: Always pick two clear points on the graph to calculate slope, ensuring accuracy!