Final answer:
The equation of the line passing through the points (-3,7) and (3,3) is y = -2/3x + 5, calculated by first finding the slope and then solving for the y-intercept. The equation of the line is then y = -2/3x + 5.
Step-by-step explanation:
To find the equation of the line passing through the points (-3,7) and (3,3), we need to determine the slope (m) and the y-intercept (b) in the formula y = mx + b. First, we calculate the slope using the formula m = (y2 - y1) / (x2 - x1), which gives us m = (3 - 7) / (3 - (-3)) = -4/6 = -2/3. Now that we have the slope, we use one of the points to solve for b. Using point (-3,7), we substitute the values into the equation y = mx + b to get 7 = (-2/3)(-3) + b, which simplifies to 7 = 2 + b, hence b = 5.
The equation of the line is then y = -2/3x + 5.