Answer:
[tex]y+ 6 = 2 (x-7)[/tex]
Step-by-step explanation:
1) Lines that are perpendicular have slopes that are opposite reciprocals of each other. y = -1/2x - 8 is in y = mx + b form, in which the number in place of m represents the slope. So, the slope of y = -1/2x - 8 is -1/2. The opposite reciprocal of it would be (remember to flip the fraction and reverse the sign) 2. So, 2 is the slope we need for the answer.
2) When you know a point that the line must pass through and its slope, you can use point-slope form ([tex]y-y_1 = m (x - x_1)[/tex]) to write an equation. [tex]x_1[/tex] and [tex]y_1[/tex] represents the x and y values of the point the line intersects, and m represents the slope. So, substitute 2 for m, 7 for [tex]x_1[/tex], and -6 for [tex]y_1[/tex].
[tex]y-(-6) = 2 (x- 7)\\y + 6 = 2 (x-7)[/tex]
