Final answer:
The equation of the line that goes through (-3, -1) and (3, 3) is y = (2/3)x + 1, which is equivalent to option c. 3x - 2y = 3.
Step-by-step explanation:
The equation of the line that goes through (-3, -1) and (3, 3) can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Calculate the slope (m) using the formula (y2 - y1) / (x2 - x1).
m = (3 - (-1)) / (3 - (-3)) = 4 / 6 = 2/3.
Step 2: Substitute the slope (m) and the coordinates of one of the points into the equation y = mx + b to solve for b.
-1 = (2/3)(-3) + b
-1 = -2 + b
b = -1 + 2 = 1.
Therefore, the equation of the line is y = (2/3)x + 1, which is equivalent to option c. 3x - 2y = 3.