Question

Find the equation of the line perpendicular to y=-4x+3 that also intersects the point (8,1)

Answer 1

Hey there! :)

Perp. to y = -4x + 3 ; intersects (8, 1)

Slope-intercept form is : y=mx+b where m = slope, b = y-intercept

So, our slope of the given equation is -4. However, our new slope is 1/4 because it is the negative reciprocal of -4. We have to use the negative reciprocal because our new line is perpendicular to our given one.

Now, using (8, 1) and our new slope (1/4), simply plug everything in to the point-slope form.

Point-slope : y-y1 = m(x - x1)

y - 1 = 1/4(x - 8)

Simplify.

y - 1 = 1/4x - 2

Add 1 to both sides.

y = 1/4x - 1 ⇒ our new equation.

Therefore, the number that fits in the question mark is -1.

~Hope I helped!~

Answer 2

-1

Explanation:

They already did the opposite reciprocal for you.

They have it in the form
`y=(1)/(4)x+b` now.

To find b you just enter (x,y)=(8,1).

Let's do that.

`1=(1)/(4)(8)+b`

`1=2+b`

Subtract 2 on both sides:

`-1=b`

b=-1