To write the equation of the line in the graph, we can use the slope-intercept form of the equation of a line:

$y = mx + b$

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 $m$

The slope of a line is the change in $y$ divided by the change in $x$, which is calculated as:

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

Looking at the graph, I will select two points on the line:

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

Now calculate the slope:

$m = \frac{4 - (-4)}{2 - (-2)} = \frac{4 + 4}{2 + 2} = \frac{8}{4} = 2$

So, the slope $m$ is 2.

Step 2: Find the y-intercept $b$

The y-intercept is the point where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at $y = 0$.

Thus, $b = 0$.

Final Equation

Now that we know $m = 2$ and $b = 0$, the equation of the line is:

$y = 2x$

Would you like further details or have any questions?

Here are some related questions:

1. How do you calculate the slope of a line from its graph?
2. What is the significance of the y-intercept in a linear equation?
3. How do you convert from slope-intercept form to standard form?
4. What does it mean if a line has a slope of zero?
5. How can you determine if two lines are parallel based on their equations?

Tip: Always check if the line crosses the y-axis at zero, as that simplifies your equation greatly by eliminating the constant $b$.