Let's start by writing down the equations of the given points in the form (x, y):
* (3, 10)
* (-2, -20)
Now, a line can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. We need to find the values of m and b that satisfy the equations of the given points.
* Using the point (3, 10), we can find the slope by dividing the difference in y-values by the difference in x-values:
m = (10 - (-20)) / (3 - -2) = -2
* Using the point (-2, -20), we can find the y-intercept by substituting the x- and y-values in the equation:
y = mx + b
-20 = -2 * (-2) + b
-20 = 4 + b
b = -24
So, the equation of the line that passes through the points (3, 10) and (-2, -20) is y = -2x - 24.