To determine the equation of the line, we will use the slope-intercept form:

$y = mx + b$

where:

• $m$ is the slope
• $b$ is the y-intercept

Step 1: Identify Two Points

From the image, two points on the line are:
$(0,2) \quad \text{and} \quad (5,6)$

Step 2: Find the Slope

The slope formula is:

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

Substituting the values:

$m = \frac{6 - 2}{5 - 0} = \frac{4}{5}$

Step 3: Determine the y-Intercept

The y-intercept $b$ is the value of $y$ when $x = 0$. From the graph, $b = 2$.

Step 4: Write the Equation

$y = \frac{4}{5}x + 2$

This is the equation of the line.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. How do you find the slope if the points have negative coordinates?
2. What happens to the equation if the line is vertical?
3. How can you determine if two lines are parallel or perpendicular?
4. How do you rewrite the equation in standard form?
5. How can you graph a line given its equation?

Tip: The slope represents the rate of change; in this case, for every 5 units moved in the x-direction, the y-value increases by 4.