Answer:
y = 3x
Step-by-step explanation:
1) Identify the slope of the given equation. We can see that the y is isolated in the equation [tex]y = -\frac{1}{3} x+5[/tex], so it is in slope-intercept form, or [tex]y = mx + b[/tex] format. When an equation is in slope-intercept form, the [tex]m[/tex], or the coefficient of the x-term, represents the slope, thus [tex]-\frac{1}{3}[/tex] is the slope of the given equation. Lines that are perpendicular to each other have slopes that are opposite reciprocals, so the slope of the new line would be 3.
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the new line. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.
Since [tex]m[/tex] represents the slope, substitute 3 for it. 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 (3,9) for those places in the formula as well. Then, with the resulting equation, isolate y to find an answer in slope-intercept form:
[tex]y-9 = 3(x-3)\\y-9 = 3x-9\\y = 3x[/tex]
