Find the x- and y-intercepts of the line that passes through the given points.
(-6,-6), (3,-3)
To find the x-intercept, we set y = 0 and solve for x.
Using the equation of the line through the two points:
(-6, -6):
0 = m(-6) + b
0 = -6m + b
(3, -3):
0 = m(3) + b
Now we have a system of equations:
0 = -6m + b
0 = 3m + b
Solving this system, we start by isolating b in both equations:
b = 6m
Substituting this back into the second equation:
0 = 3m + 6m
0 = 9m
m = 0
Substituting m = 0 back into the first equation:
0 = -6(0) + b
0 = b
So the equation of the line is y = 0x + 0 which simplifies to y = 0.
Therefore, the x-intercept is 0.
To find the y-intercept, we set x = 0 and solve for y.
Using the equation of the line through the two points:
(-6, -6):
y = m(-6) + b
-6 = -6m + b
(3, -3):
-3 = 3m + b
Now we have a system of equations:
-6 = -6m + b
-3 = 3m + b
Solving this system, we start by isolating b in both equations:
b = 6m - 6
Substituting this back into the second equation:
-3 = 3m + 6m - 6
-3 = 9m - 6
3 = 9m
m = 1/3
Substituting m = 1/3 back into the first equation:
-6 = -6(1/3) + b
-6 = -2 + b
b = -4
So the equation of the line is y = (1/3)x - 4.
Therefore, the y-intercept is -4.