The line in the graph is straight, and we can find its equation using the slope-intercept form of a line, which is:

$y = mx + b$

Where:

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

1. Calculate the Slope ($m$):

The slope $m$ is the "rise over run," calculated as:

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

Looking at two points from the graph, let's choose the points $(2, 5)$ and $(-2, -3)$.

Using these points: $m = \frac{5 - (-3)}{2 - (-2)} = \frac{5 + 3}{2 + 2} = \frac{8}{4} = 2$

So, the slope of the line is $m = 2$.

2. Find the y-intercept ($b$):

The y-intercept is the value of $y$ when $x = 0$. Observing the graph, the line crosses the y-axis at $(0, 1)$, so $b = 1$.

3. Write the Equation:

With $m = 2$ and $b = 1$, the equation of the line is:

$y = 2x + 1$

This is the equation of the line shown in the graph.

Would you like more details or have any further questions?

Here are 5 related questions:

1. How do we calculate the slope if the graph is not clearly marked?
2. What if the line passes through more complicated points like fractions?
3. Can we calculate the slope using a different formula or method?
4. How do we find the equation of a line if it’s vertical or horizontal?
5. What is the general form of a linear equation, and how does it relate to the slope-intercept form?

Tip: When calculating the slope, always ensure that the points you choose are distinct and easy to read from the graph for better accuracy.