Given δabc with a(-6, -1), b(3, 7), and c(4, -6), write the equation of the line containing the altitude that passes through b in slope-intercept form. show all work, and graph the triangle and the altitude.
slope intercept: y = mx + b

Given ΔABC with A(-6, -1), B(3, 7), and C(4, -6)

Since it is an altitude and pass thru B, then it is perpendicular to AC. 
so slope(AC) = (-1 +6)/(-6 - 4) = -5/10 = -1/2

perpendicular lines, slope is opposite and reciprocal
so slope = 2

passes through B(3, 7)

y - 7 = 2(x - 3)
y - 7 = 2x - 6
y = 2x + 1

equation in slope intercept form:
y = 2x + 1