Answer: [tex]y = -\frac{1}{6}x + \frac{7}{2}[/tex]
Step-by-step explanation:
The slope of the line perpendicular is always the negative reciprocal of the line you're given.
So, in this case, the slope in y = 6x + 4, is 6 (the coefficient in front of the x). The negative of this is -6, and then do the reciprocal which is -1/6.
Next, we are given the the point that it passes through, which is (-3, 4). We have to use point slope formula for this which is given by:
[tex]y - y_{1} = m(x-x_{1})[/tex]
We know m = -1/6 from before, and [tex]x_{1} = -3[/tex], and [tex]y_{1} = 4[/tex] (this comes from the given point). Plugging these in we have:
[tex]y - 4 = -\frac{1}{6} (x - (-3))[/tex]
Point slope intercept form is given by [tex]y = mx + b[/tex] so to rearrange it to this form, we have to distribute the -1/6 and isolate y.
After distributing we get:
[tex]y - 4 = -\frac{1}{6}x -\frac{1}{2}[/tex]
Then isolating the y term we get:
[tex]y = -\frac{1}{6}x + \frac{7}{2}[/tex]
