Final answer:
To find the equation perpendicular to y = -2x - 10 through the point (10, 7), determine the slope of the given equation, find the negative reciprocal of that slope, and use the point-slope form of a linear equation to write the equation of the perpendicular line.
Step-by-step explanation:
To find the equation perpendicular to y = -2x - 10 through the point (10, 7), we need to determine the slope of the given equation and then find the negative reciprocal of that slope to get the slope of the perpendicular line. The given equation y = -2x - 10 has a slope of -2. The negative reciprocal of -2 is 1/2. So, the slope of the perpendicular line is 1/2. Using the point-slope form of a linear equation, we can write the equation as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the given values, we have y - 7 = (1/2)(x - 10). Simplifying this equation, we get y = (1/2)x - 3. Therefore, the equation perpendicular to y = -2x - 10 through the point (10, 7) is y = (1/2)x - 3.