Answer:
Please check the explanation.
Step-by-step explanation:
6)
Given the line
[tex]y=-\frac{1}{3}x+3[/tex]
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the line and b is the y-intercept
Thus, the slope of line = -1/3
We know that parallel lines have the same slope.
Hence, the slope of the parallel line is also m=-1/3
So, substituting m = -1/3 and (3, 1) in the slope-intercept form to find the y-intercept
[tex]y=mx+b[/tex]
[tex]1=\frac{-1}{3}\left(3\right)+b[/tex]
Switch sides
[tex]\frac{-1}{3}\left(3\right)+b=1[/tex]
[tex]-1+b=1[/tex]
[tex]b=2[/tex]
Thus, the equation line in slope-intercept form
[tex]y=mx+b[/tex]
[tex]y=-\frac{1}{3}x+2[/tex]
8)
Given the line
[tex]y=\frac{1}{4}x+1[/tex]
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the line and b is the y-intercept
so the slope of line = 1/4
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: -4
Thus, subtituting m = -4 and (-1, 4) in the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-4=-4\left(x-\left(-1\right)\right)[/tex]
writing the point-slope form in the slope-intercept form
[tex]y-4=-4\left(x+1\right)[/tex]
add 4 to both sides
[tex]y-4+4=-4\left(x+1\right)+4[/tex]
[tex]y=-4x[/tex]
