Final answer:
The correct option is A. y = 3x + 1.
Step-by-step explanation:
To find the equation of the line that passes through the points (-1,-2) and (3,10), you need to determine the slope (m) and the y-intercept (b) of the line using the slope-intercept form of a line, which is y = mx + b.
The slope (m) is calculated as the change in y divided by the change in x between the two points:
m = (y2 - y1) / (x2 - x1)
Applying the coordinates of the given points:
m = (10 - (-2)) / (3 - (-1))
m = 12 / 4 = 3
Now that we have the slope, we can plug the slope and either of the points into the slope-intercept form to solve for the y-intercept (b). Using point (-1,-2):
-2 = 3(-1) + b
-2 = -3 + b
b = -2 + 3
b = 1
Thus the equation of the line can be written as:
y = 3x + 1
Therefore, the correct answer is A) y = 3x + 1.