Answer (assuming it can be in slope-intercept form):
[tex]y = -3x + 5[/tex]
Step-by-step explanation:
Lines that are perpendicular to each other have slopes that are opposite reciprocals of each other.
1) First, identify the slope of the given equation. The y is isolated, so it's in slope-intercept form, as represented by the formula [tex]y = mx + b[/tex]. The coefficient of the x-term, or [tex]m[/tex], represents the slope. Thus, by looking at the equation, its slope is [tex]\frac{1}{3}[/tex]. The opposite reciprocal of that is [tex]-3[/tex]. So, [tex]-3[/tex] will be the slope of the new equation.
2) Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the new line. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
[tex]m[/tex] represents the slope, so substitute [tex]-3[/tex] in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, so substitute the x and y values of (1,2) into the formula as well. From there, isolate y to find the slope-intercept equation of the perpendicular line.
[tex]y -2 = -3(x-1)\\y-2 = -3x+3\\y = -3x + 5[/tex]
