To find the equation of the line shown in the image, we need to follow these steps:

Step 1: Identify the coordinates of two points on the line.

From the image, the two points appear to be:

• Point 1: $(-6, -2)$
• Point 2: $(2, 2)$

Step 2: Calculate the slope of the line.

The slope $m$ of the line is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of the two points: $m = \frac{2 - (-2)}{2 - (-6)} = \frac{2 + 2}{2 + 6} = \frac{4}{8} = \frac{1}{2}$ So, the slope of the line is $\frac{1}{2}$.

Step 3: Use the point-slope form of the equation of a line.

The point-slope form is given by: $y - y_1 = m(x - x_1)$ We can use one of the points, say $(-6, -2)$, and the slope $\frac{1}{2}$: $y - (-2) = \frac{1}{2}(x - (-6))$ Simplifying: $y + 2 = \frac{1}{2}(x + 6)$ Distribute the slope: $y + 2 = \frac{1}{2}x + 3$ Subtract 2 from both sides to solve for $y$: $y = \frac{1}{2}x + 1$

Final Answer:

The equation of the line is: $y = \frac{1}{2}x + 1$

Would you like more details or have any questions about the steps?

Here are 5 related questions to further your understanding:

1. How do you find the slope if the coordinates are given in fraction form?
2. What is the general formula for the slope of a line?
3. Can you derive the equation using a different point on the line?
4. How does changing the slope affect the line's steepness?
5. What is the y-intercept of this line, and how do you interpret it?

Tip: Remember that the slope of a line indicates its steepness and direction. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.