Explanation:
the general line equation is
y = ax + b
a is the slope of the line. it is always the factor of x expressed as ratio y/x. it indicates how many units y changes, when x changes a certain amount of units when going from one point to another.
b is the y-intercept (the y value when x = 0).
so, let's use the 2 given points to find a and b.
(3, 1) to (0, 10)
x changes by -3 units (from 3 to 0).
y changes by +9 units (from 1 to 10).
so, the slope a is 9/-3 = -3
and to get b we would simply pick one point and use its coordinates as x and y values and then solve for b. but the second point gives us already the solution, as its x coordinate is 0 (and therefore its y coordinate is b).
so, the line equation is
y = -3x + 10