PIL import Image

Open and display the uploaded image

image_path = "/mnt/data/1734375185808n8capv3i.jpg" img = Image.open(image_path) img.show()To write the equation of the line in slope-intercept form, which is $y = mx + b$, we need:

1. The slope $m$:

   • The slope is the change in $y$ divided by the change in $x$ (rise over run).

2. The y-intercept $b$:

   • This is the value of $y$ where the line crosses the $y$-axis.

Step 1: Identify two points on the line

From the graph:

• Point 1: $(0, 10)$ (the line crosses the $y$-axis here)
• Point 2: $(3, 1)$

Step 2: Calculate the slope $m$

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points $(0, 10)$ and $(3, 1)$: $m = \frac{1 - 10}{3 - 0} = \frac{-9}{3} = -3$

Step 3: Write the equation

The slope-intercept form is $y = mx + b$, where $m = -3$ and $b = 10$. Substituting these values: $y = -3x + 10$

Final Answer:

The equation of the line is: $y = -3x + 10$

Do you want further explanations or have questions about any step? Let me know!

Related Questions:

1. What is the general formula for slope-intercept form of a line?
2. How do you find the slope given two points?
3. What happens when the slope is positive or zero?
4. How can you determine the equation of a horizontal line?
5. How do you graph a line given its equation?

Tip: The slope tells you how steep a line is; a negative slope means the line decreases from left to right.