The image shows a graph of a line, and the task is to write the equation of the line in slope-intercept form. The slope-intercept form of a line is written as:

$y = mx + b$

Where:

• $m$ is the slope of the line
• $b$ is the y-intercept (the point where the line crosses the y-axis)

Step 1: Find the slope $m$

To find the slope, we use the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph, we can identify two points on the line:

• Point 1: $(-10, 2)$
• Point 2: $(0, 4)$

Now, applying the formula for slope:

$m = \frac{4 - 2}{0 - (-10)} = \frac{2}{10} = \frac{1}{5}$

Step 2: Find the y-intercept $b$

The y-intercept is the value of $y$ when $x = 0$. From the graph, it's clear that the line crosses the y-axis at $y = 4$. Thus, $b = 4$.

Final Equation

Substituting the values of $m = \frac{1}{5}$ and $b = 4$ into the slope-intercept form:

$y = \frac{1}{5}x + 4$

This is the equation of the line.

Would you like more details or explanations on any step? Here are some related questions for further practice:

1. How do you find the slope of a line when given two points?
2. How does changing the slope affect the graph of a line?
3. What happens to the graph if the y-intercept changes?
4. Can you convert a line in slope-intercept form to standard form?
5. How can you graph a line using only its slope and y-intercept?

Tip: When graphing a line from its equation, always start by plotting the y-intercept and then use the slope to find other points.