point slop from equation is 5x8y9=0 and it passes thru (1,6)
Algebra

Tutor: None Selected  Time limit: 1 Day 
equation
Thank you for the opportunity to help you with your question!
First, we solve the given equation for y in order to find its slope. So we would have the following:
5x  8y  9 = 0 (adding 8y from both sides) > 5x  8y + 8y  9 = 0 + 8y > 5x  9 = 8y
5x  9 = 8y (dividing by 8 from both sides) > 5x/8  9/8 = 8y/8 > 5/8x  9/8 = y
So finally, we have: y = 5/8x  9/8. And let's remember the slopeintercept form is: y = mx + b (where m is the slope and b is the yintercept). Then we have:
If we compare y = mx + b with y = 5/8x + b we can see that the slope is m = 5/8. Ok, then if it says that the lines are parallel we use the same slope. By the way, let's remember that the slopepoint form is:
y  y1 = m(x  x1) ; where: x1 and y1 are the coordinates of the given point.
Since the given point is: (1 , 6) then x1 = 1 and y1 = 6 and we already know that the slope is m = 5/8. So we enter them into the formula and we have:
y  y1 = m(x  x1) > y  6 = 5/8(x (1) ) > y  6 = 5/8(x + 1) This is the pointslope form.
We could leave it to the slopeintercept form by solving for y like this:
y  6 = 5/8(x + 1) > y  6 = 5/8x + 5/8 > y  6 + 6 = 5/8x + 5/8 + 6 > y = 5/8x + 5/8 + 6*8/8
y = 5/8x + 5/8 + 48/8 > y = 5/8x + 53/8 This is the interceptslope form.
If it says that the lines are perpendicular then you will need to find the perdicular slope respect to the slope 5/8. For that, we flip the fraction and we multiply by 1. So we have the following:
5/8 > 8/5 > (1)(8/5) > m = 8/5 (perpendicular slope).
Then we use the same formula (remember x1 = 1 and y1 = 6 from the given point):
y  y1 = m(x  x1) > y  6 = 8/5(x  (1) ) > y  6 =  8/5(x + 1) This is the pointslope form.
y  6 = 8/5x  8/5 > y  6 + 6 = 8/5x  8/5 + 6 > y = 8/5x + 22/5
Please let me know if you have any doubt or question.
Secure Information
Content will be erased after question is completed.