precalulucs hw im stuck

Question

Write an equation for a line perpendicular to  and passing through the point (8,3) =   

Answer 1

Hi, Jason!

To write the equation of a perpendicular line, you have to take the given slope of the first equation and 1) turn it into its reciprocal, and 2) multiply it by -1.

To find a number's reciprocal, we need to put it in fraction form (if it isn't already) and then flip the fraction over. The slope of our given equation is 4, and this can also be written as 4/1 (since anything divided by 1 is itself!)

Now that we have a fraction (4/1), we can flip it over to give us 1/4. That's all we need to do to find the reciprocal.

The second step is to multiply the 1/4 by -1, which simply gives us -1/4. Both steps are now completed, so we know that -1/4 is the slope of our perpendicular line!

But we're not done just yet - we need to write the equation of the line that passes through the point (8, 3). We can use the formula y = mx + b (with x and y representing the points, m representing the slope, and b representing the y-intercept) to fill in the blanks and determine what we don't know.

We can use our point (8, 3) for x and y respectively, and for m, we can use our new slope, -1/4. After plugging these numbers into the formula, we have:

3 = (-1/4)(8) + b

To start solving for b, let's multiply the -1/4 and 8 together:

-1/4 • 8 = -8/4 = -2

Now we have:

3 = -2 + b

Let's add 2 to both sides, to isolate b:

3 = -2 + b

+2 +2

5 = b

We're left with b = 5. Now we can form an equation for the line perpendicular to the given line, which passes through the given point, because we've found a new m (slope) and a new b (y-intercept). All you have to do is plug those into your formula, y = mx + b.

Hope this helps!

Answer 2

a perpendicular line has the negative inverse for the slope. Negative inverse of 4 is -1/4. change the sign and flip the fraction upside side: 4 = 4/1. flip it upside down you get 1/4, then changer the sign: -1/4

y= -(1/4)x + b, solve for b by plugging in the point (8,3)

3 = -(1/4)(8) + b

b = 3+2 = 5

y=-x/4 +5 is the perpendicular line through the given point