Note: this answer assumes the equation of the line can be put in slope-intercept form.
Answer:
[tex]y + 3 = \frac{1}{2}(x-6)[/tex]
Step-by-step explanation:
1) First, find the slope of y + 7 = -2 (x - 6). We can see that it's already in point-slope form, or [tex]y-y_1 = m (x-x_1)[/tex] format. Remember that the number in place of the [tex]m[/tex] is the slope. Therefore, -2 is the slope of that equation.
What we need is the slope that is perpendicular to that, though. So, find the opposite reciprocal of -2. To do this, change its sign, convert it into a fraction ([tex]-\frac{2}{1}[/tex]), and flip its numerators and denominators. Therefore, the perpendicular slope would be [tex]\frac{1}{2}[/tex].
2) Now that we have a slope and a point the line passes through, we can write an equation using the point-slope formula, [tex]y-y_1 = m (x-x_1)[/tex]. In order to write an equation, the [tex]x_1[/tex], [tex]y_1[/tex], and [tex]m[/tex] have to be substitute for with real values.
The [tex]m[/tex] represents the slope. We already calculated that in the last step, so put [tex]\frac{1}{2}[/tex] in place of the [tex]m[/tex]. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line passes through. We know that the line has to pass through (6, -3), so substitute 6 for [tex]x_1[/tex] and -3 for [tex]y_1[/tex]:
[tex]y - (-3) = \frac{1}{2}(x -(6))\\y + 3 = \frac{1}{2}(x - 6)[/tex]
Therefore, (again, assuming that the line can be put in point-slope form) the answer is [tex]y + 3 = \frac{1}{2}(x-6)[/tex].
