Final answer:
To find the equation of the line perpendicular to the one passing through (12, -15) and (22, 10), calculate the negative reciprocal of the slope of the original line and use the point-slope form with the given point (12, 16). The equation of the perpendicular line is y = -0.4x + 20.8.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line and passes through a given point, first, we need to determine the slope of the original line using the two points provided, which are (12,-15) and (22,10). The slope of this line is:
m = (10 - (-15)) / (22 - 12) = 25 / 10 = 2.5
A line perpendicular to this will have a slope that is the negative reciprocal of 2.5, so the slope of the perpendicular line will be m = -1 / 2.5 = -0.4.
Now, using the point (12, 16) that the perpendicular line passes through and the slope we just found, we can use the point-slope form of a line equation: y - y₁ = m(x - x₁). Plugging in the point and the slope:
y - 16 = -0.4(x - 12)
Expanding this,
y = -0.4x + 4.8 + 16
y = -0.4x + 20.8
Thus, the equation of the line perpendicular to the line passing through (12, -15) and (22, 10) that goes through point (12, 16) is y = -0.4x + 20.8.