Final answer:
The linear equation that describes the line passing through the points (-3, 2), (0, 4), and (3, 6) on a coordinate plane is y = (2/3)x + 4, calculated by determining the slope and y-intercept.
Step-by-step explanation:
The question asks to determine which equation describes the line graphed through the points (-3, 2), (0, 4), and (3, 6). To find the equation of this line, we can calculate the slope (m) and the y-intercept (b) of the line. The slope can be found by taking two of the points and using the formula m = (y2 - y1) / (x2 - x1). Taking the points (0, 4) and (3, 6), the slope would be (6 - 4) / (3 - 0) = 2 / 3. Now that we have the slope, we can use one of the points to solve for the y-intercept (b) in the linear equation y = mx + b. Plugging in the point (0, 4), where x=0 and y=4, gives us the equation 4 = (2/3)(0) + b, simplifying to b = 4. Therefore, the equation of the line is y = (2/3)x + 4.