Answer:
[tex]y = -\frac{1}{13} x+\frac{27}{13}[/tex]
Step-by-step explanation:
1) First, find the slope of the given line. Since the equation has y isolated and it is in a [tex]y = mx + b[/tex] format, it must be in slope-intercept form. The number in place of [tex]m[/tex], or the coefficient of the x-term, represents the slope. So, the slope of this line must be 13.
Lines that are perpendicular have slopes that are opposite reciprocals. So, the slope of the perpendicular line must be [tex]-\frac{1}{13}[/tex].
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute the found values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex]. This gives the equation of the line in point-slope form. (We can convert it to slope-intercept form later.)
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{1}{13}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (1,2) into the formula as well. Then, with the resulting equation, isolate y to find the equation of the line in slope-intercept form:
[tex]y-2 = -\frac{1}{13} (x-1)\\y -2 = -\frac{1}{13} x+\frac{1}{13} \\y = -\frac{1}{13} x+\frac{1}{13} +\frac{26}{13} \\y = -\frac{1}{13} x+\frac{27}{13}[/tex]
