Answer:
y -5 = -3/2(x +5)
Step-by-step explanation:
The altitude from B is perpendicular to segment AC. The slope of segment AC is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-5))/(2 -(-7)) = 6/9 = 2/3
The slope of the altitude line will be the opposite reciprocal of this, so is ...
-1/m = -1/(2/3) = -3/2
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -5 = -3/2(x +5) . . . . . line with slope -3/2 through B(-5, 5)
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Additional comment
The equation can be put in other forms, as you may wish. Solving for y gives the slope-intercept form.
y = -3/2x -5/2 . . . . . slope-intercept form
3x +2y = -5 . . . . . . . standard form
