Answer:
a) [tex]y=-\frac{1}{9}x[/tex]
b)[tex]y-2=-\frac{1}{3} (x-1)[/tex]
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and can find the slope.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
a) [tex]m\neq 9[/tex] in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{1}{9}[/tex].
We will substitute [tex]m=-\frac{1}{9}[/tex] and [tex]x_1=0\\y_1=0[/tex].
[tex]y-0=-\frac{1}{9} (x-0)[/tex]
This simplifies to:
[tex]y=-\frac{1}{9}x[/tex]
b) The equation y=3x+4 follows y=mx+b. For the perpendicular line, [tex]m\neq 3[/tex]. We will need to change it into its negative reciprocal which is [tex]m=-\frac{1}{3}[/tex].
We will substitute [tex]m=-\frac{1}{3}[/tex] and [tex]x_1=1\\y_1=2[/tex].
[tex]y-2=-\frac{1}{3} (x-1)[/tex]
