Instructions: Find the equation of the line through point (8, - 9) and perpendicular to 3x + 8y = 4 4. Use a forward slash (ie. for fractions (e.g. 1/2 for .

Answer 1

First we can find the slope of the second line.

Let's rewrite the equation as 8y=44-3x.

After dividing both sides of the equation by 8 we'll get an equivalent equation y = 5.5 - 3/8 * x.

The coefficient of x is the slope -> the slope is -3/8.

In order for the line to be perpendicular to this line the product of the slopes of two lines should be equal to -1 or in other words the slopes have to be opposite reciprocals of each other. The reciprocal of -3/8 is -8/3. Opposite to it is 8/3.

Now we know the slop and the coordinates of a point on the line (given). Let's make the equation of the line in the form of y = mx+ b. We can plug in values for m, y and x. m = 8/3(slope), y=-9 (second coordinate of the point), x = 8 (first coordinate). We got

-9 = 8/3 * 8 +b

Now we need to solve the equation to find b

b =-91/3 or -30 1/3

It means the equation is

y = 8/3 * x - 30 1/3

or we can make it look better and multiply both sides by 3 to get rid of the fractions

3y = 8x - 91

You can check this answer by plotting both graphs on the coordinate plane and see if they are perpendicular and if point (8,-9) belongs to this line.

Answer 2

The slope of a line in standard form ax + by = c is -a/b.

For 3x + 8y + 4, -a/b = -3/8.

The slope of a perpendicular line is the negative reciprocal of of -3/8 = 8/3

The point-intercept equation of a line is y-y1 = m(x - x1), where m is the slope and (x1,y1) is a point on the line.

here m = 8/3 and (x1,y1) = (8,-9)

y--9 = 8/3(x-8)

y+9 = 8/3x - 64/3

3y + 27 = 8x - 64

8x -3y = 81