The problem asks to find the equation of the line that is graphed on the coordinate plane. To determine this equation, we'll use 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).

Step 1: Find the Slope ($m$)

From the graph, we can identify two points on the line:

• Point 1: $(-2, 0)$
• Point 2: $(2, 3)$

To calculate the slope, use the slope formula:

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

Substitute the coordinates:

$m = \frac{3 - 0}{2 - (-2)} = \frac{3}{4}$

So, the slope $m$ is $\frac{3}{4}$.

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

We already know one point on the y-axis: $(-2, 0)$, but it's better to use the slope and a specific point to find $b$. Let's use the point $(2, 3)$ and the equation $y = mx + b$.

Substitute $x = 2$, $y = 3$, and $m = \frac{3}{4}$:

$3 = \frac{3}{4}(2) + b$

Simplify:

$3 = \frac{6}{4} + b$

$3 = 1.5 + b$

Now, solve for $b$:

$b = 3 - 1.5 = 1.5$

Step 3: Write the Equation of the Line

Now that we know the slope $m = \frac{3}{4}$ and the y-intercept $b = 1.5$, the equation of the line is:

$y = \frac{3}{4}x + 1.5$

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. How do you calculate the slope if you're given two points on a line?
2. What does the slope of a line represent in real-world situations?
3. How can you find the equation of a line if you only know the slope and one point?
4. What is the significance of the y-intercept in the equation of a line?
5. How would you graph a line if you are only given its equation in slope-intercept form?

Tip: Always double-check the points you choose on a graph, as small inaccuracies can affect your calculation of the slope.