To find the slope of the perpendicular line, we must find the slope of the line with x-intercept of 2 and y-intercept of -4.
Let's use rise/run to find the slope. The run is 2, and the rise if 4 (yes, positive 4).
4/2 = 2
So, the slope of the original line is 2. The other line must have a slope that is the negative reciprocal of that, which will be -1/2.
Let's start making our equation by using point-slope form.
For a line with slope m and that passes through [tex](x_1,y_1)[/tex], the point slope form equation is the following:
[tex]y-y_1=m(x-x_1)[/tex]
We know the passing point and the slope. Now, let's plug them into the point-slope form formula.
[tex]y-4=- \frac{1}{2} (x+6)[/tex]
Distribute.
[tex]y-4= -\frac{1}{2} x-3[/tex]
Now, add both sides by 4.
[tex]y= -\frac{1}{2} x+1[/tex]
Replace y with f(x)
[tex]f(x)=- \frac{1}{2}x+1[/tex]
