Final answer:
The equation of the line that passes through the points (-3, -2) and (3, 6) is y = (4/3)x + 2.
Step-by-step explanation:
To find the equation of the line that passes through the points (-3, -2) and (3, 6), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope: m = (y2 - y1)/(x2 - x1) = (6 - (-2))/(3 - (-3)) = 8/6 = 4/3.
Next, we can pick one of the given points, for example (-3, -2), and substitute the values into the equation to solve for b: -2 = (4/3)(-3) + b. Solving for b, we get b = -2 + 4 = 2.
Therefore, the equation of the line that passes through the points (-3, -2) and (3, 6) is y = (4/3)x + 2, which corresponds to option B.