Final answer:
The equation in slope-intercept form of the line that is perpendicular to y = -1/2x + 10 and passes through the point (2, 6) is y = 2x - 2.
Step-by-step explanation:
In order to find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the given line.
The given line is y = -1/2x + 10. The slope of this line is -1/2.
The negative reciprocal of -1/2 is 2. So, the slope of the perpendicular line is 2.
Now we can use the point-slope form of a line to find the equation of the perpendicular line. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Using the point (2, 6) and a slope of 2, we have y - 6 = 2(x - 2). Simplifying this equation gives us y = 2x - 2.
Therefore, the equation in slope-intercept form of the line that is perpendicular to y = -1/2x + 10 and passes through the point (2, 6) is y = 2x - 2 (option a).