The image shows a graph where the task is to find the equation of a line passing through two points. Let's extract the coordinates of the two points to determine the equation of the line.

From the image, the two points on the line appear to be approximately:

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

Steps to find the equation of the line:

1. Find the slope (m) using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points: $m = \frac{4 - (-4)}{2 - (-2)} = \frac{8}{4} = 2$

2. Use the point-slope form of the equation of a line: $y - y_1 = m(x - x_1)$ Let's use Point 1 $(-2, -4)$: $y - (-4) = 2(x - (-2))$ Simplifying: $y + 4 = 2(x + 2)$ Expand and solve for $y$: $y + 4 = 2x + 4$ Subtract 4 from both sides: $y = 2x$

Final equation of the line:

$y = 2x$

Would you like more details on any step, or do you have any questions?

Related Questions:

1. How do you find the equation of a line if given a different pair of points?
2. What happens to the slope if the points are reversed?
3. How can we verify that the points lie on the calculated line?
4. Can we express the equation in another form, like standard form $Ax + By = C$?
5. How does the slope of a line relate to its steepness?

Tip:

Always cross-check your slope calculation using the formula, as small errors in identifying the coordinates can change the outcome.