Area of Triangle Bounded By Line

A line of positive slope m passes through the point (-2,1). Show that the area of the triangle bounded by this line and the axes is (2m + (1/2m)) + 2.

By using the slope m and the point (-2, 1), we can find the equation of the line using point-slope form.

y - y1 = m(x - x1)
y - 1 = m(x - (-2)) iff
y - 1 = m(x + 2) iff
y = m(x + 2) + 1

The base and the height of the resulting triangle corresponds to the x and y-intercepts respectively. So to find those measure, we let y = 0 and x = 0.

y = m(x + 2) + 1
0 = m(x + 2) + 1 iff
m(x + 2) = -1 iff
x + 2 = -1/m iff
x = -1/m - 2

Thus (-1/m - 2, 0) is the x-intercept and we can use this as the length of the base.

y = m(x + 2) + 1
y = m(0 + 2) + 1 iff
y = 2m + 1

Thus (0, 2m + 1) is the y-intercept and we can use this as the he