Find the x- and y-intercepts of the line that passes through the given points.
(-6,-6), (6,-2)
To find the x-intercept, we need to find the value of x when y is equal to zero.
Using the slope-intercept form of a linear equation, y = mx + b, we can first find the slope of the line passing through the given points:
m = (y2 - y1) / (x2 - x1) = (-2 - (-6)) / (6 - (-6)) = (-2 + 6) / (6 + 6) = 4 / 12 = 1/3
Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), to find the equation of the line:
Using the point (6,-2):
y - (-2) = (1/3)(x - 6)
y + 2 = (1/3)x - 2
y = (1/3)x - 4
To find the x-intercept, we set y equal to zero:
0 = (1/3)x - 4
(1/3)x = 4
x = 12
Therefore, the x-intercept is 12.
To find the y-intercept, we need to find the value of y when x is equal to zero.
Again, using the equation y = (1/3)x - 4:
y = (1/3)(0) - 4
y = -4
Therefore, the y-intercept is -4.