Final answer:
The equation of the line passing through points A(-5,-4) and B(1,6) is y = (5/3)x + 13/3, found by calculating the slope between the two points and using one of the points to solve for the y-intercept.
Step-by-step explanation:
The equation of the line passing through points A(-5,-4) and B(1,6) can be found using the formula for a straight line, which is y = mx + b, where m is the slope and b is the y-intercept. To find the slope (m), use the formula m = (y2 - y1) / (x2 - x1). So, the slope m is (6 - (-4)) / (1 - (-5)) = 10 / 6 = 5/3. Next, use one of the points, A(-5,-4), to solve for the y-intercept b: -4 = (5/3)(-5) + b. This simplifies to b = -4 + 25/3, which simplifies further to b = -12/3 + 25/3, so b = 13/3. Thus, the equation of the line is y = (5/3)x + 13/3.