you might need: calculator\nwrite an equation that represents the line.\nuse exact numbers.

Answer:

$y = \frac{2}{3}x + \frac{4}{3}$

Explanation:

Step1: Identify two points on the line.

From the graph, we can identify two points on the line: $(1, 2)$ and $(4, 4)$. Let $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (4, 4)$.

Step2: Calculate the slope of the line.

The slope $m$ is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. $$m = \frac{4 - 2}{4 - 1} = \frac{2}{3}$$

Step3: Determine the y-intercept.

Use the slope-intercept form $y = mx + b$ and one point, say $(1, 2)$, along with the slope $m = \frac{2}{3}$. $$2 = \frac{2}{3}(1) + b$$ $$2 = \frac{2}{3} + b$$ $$b = 2 - \frac{2}{3} = \frac{6}{3} - \frac{2}{3} = \frac{4}{3}$$

Step4: Write the equation of the line.

Substitute the slope $m = \frac{2}{3}$ and the y-intercept $b = \frac{4}{3}$ into the slope-intercept form $y = mx + b$. $$y = \frac{2}{3}x + \frac{4}{3}$$