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shawnkat
Hey there!

First, let's look at what perpendicular means. Imagine a cross, where there's all 90 degree angles. That's exactly what we're talking about when we say perpendicular. The given equation is in slope-intercept form, where we have:

y = mx + b
where m is the slope and b is the y-intercept.

When we're writing an equation with a perpendicular slope, we use the negative reciprocal of the given slope. Thus, we can make 0.3 1/3, and take the reciprocal to make 3, and make it negative 3 as it's the negative reciprocal. Now, we know we have a line with the slope of -3 and goes through (-3, 8). We can use the x and y values in this set of points, along with the slope, to create an equation to solve for b. That gives us:

8 = -3(-3) + b
8 = -9 + b
17 = b

Now, since we have slope and y-intercept, we can write our equation as:

y = -3x + 17

Hope this helps!
calculista

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1\\m2=-1/m1[/tex]

in this problem the slope of the given line is

[tex]m1=-0.3=-\frac{3}{10}[/tex]

the value of m2 is

[tex]m2=-1/(-3/10)=\frac{10}{3}[/tex]

with the point [tex](3,-8)[/tex] and the slope m2 find the equation of the line

the equation of the line in the form point-slope is

[tex]y-y1=m*(x-x1)[/tex]

substitute the values

[tex]y+8=\frac{10}{3}*(x-3)[/tex]

[tex]y=\frac{10}{3}x-10-8[/tex]

[tex]y=\frac{10}{3}x-18[/tex]

therefore

the answer is

[tex]y=\frac{10}{3}x-18[/tex]

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