Please help asap! Math

[KiKiPie]

Bryson and I have been sick with the flu all week. So of course I waited until the last minute to try to figure this out and its due tonight. Can someone Please please please help me with this??


2. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 2y = 8 and passing through (1, -6

[Connie]

I just emailed this to my son...he's a math whiz. I'm not sure if he's still up and will get it tonight, but I'll let you know if I hear back!

[KiKiPie]

Originally Posted by Connie

I just emailed this to my son...he's a math whiz. I'm not sure if he's still up and will get it tonight, but I'll let you know if I hear back!

Connie you are so sweet!

[BLEU BOY BARBER]

no answer I was horrible at math and my son is away tonight or I would ask him.. I feel for you


These kids have hard stuff these days.. I have one in first grade and even that homework is hard for me and my hubby it takes both of us and we still go to the teacher go figure

Extra Hug

[BLEU BOY BARBER]

I googled your exact question and this is what I got see if this helps!!! WHEN ALL ELSE FAILS GOOGLE HEHE



Question
I have a question that says:
Find the equation, in standard form, with all integer coefficients, of the line perpendicular to 4x – 2y = 10 and passing through (8, 5).

What do they mean, and do I have to graph multiple slopes?


Answer
Hi Athena,

The question asks us to find an equation for a normal (a line which is perpendicular) to the straight line 4x+2y=10. After we have worked out the equation, we have to put it in standard form, with integer coefficients. (for example, if we consider the equation fro a straight line a*x+b*y+c=0, the question requires that the coefficients "a", "b" and constant "c" must all be integers)

To answer this question, you need to know:
i) how to find the slope (or gradient) of a stright line described by a given equation.
ii) understand that a normal, say, y=nx+c, (which is always at 90 degrees relative to the given equation y=mx+b) has a slope "n" which satisfies the following condition: m*n=-1. This implies that the slope of the normal is related to the slope of the given line by n=-1/m....[#1]
iii) once the slope of the normal has been evaluated, determine the equation of the normal using a point which lies on the normal.

Solution:
i) From 4x+2y=10, we rearrange the equation making y the subject. Intermediate step is 2y=-4x+10, dividing throughout by 2 gives y=-2x+5. Comparing this to y=mx+b, we note that m=-2 and b=5. We interpret "m" as the slope of the given line, and "b" as the y-intercept (where the line crosses the y-axis when x=0).

ii) The gradient of the normal is n=-1/m=1/2. So, we know that the normal has the form y=nx+c, where n=0.5.

iii) Finally, if the normal passes through (8,5), this must satisfy the equation in (ii).
Substituting x=8,y=5 into y=nx+c, (with n=0.5) we get 5=0.5*8+c. Thus, c=1.

The equation of the normal is now fully determined.
Normal equation: y=0.5x+1. ...[#2]

iv) Read the instructions very carefully. We cannot leave the answer in this form, because the question asks for integer coefficients, in standard form.
Multiplying [#2] by 2 on both sides, we readily obtain 2y=x+2. It's now a matter of rearranging this into x-2y+2=0.

Learn this process well, so that you can tackle similar questions.

Cheers

[Tillys_mom]

My hubby said this....

first get the original equation into the form y=mx+b with m being the slope of the line and b being the y intercept. To do this solve the original equation for y. The equation in this form will then look like y=-1/2x+4. When 2 lines are perpendicular the slopes when multiplied together equal -1. Since the slope of your original line is -1/2 the slope of the new line is 2. Then to determine the y intercept of the new line you will use the point which the line passes through (1,-6) and the slope, which was 2. Plug 1 in for x, -6 in for y and 2 in for m in y=mx+b. B with then be equal to -4. Therefore the equation for the new line will be y=2x-4. Then put this equation back into standard form by getting both the x and y terms on the same side of the equation, it will then look like, 2x-y=4.

[Tillys_mom]

Originally Posted by Tillys_mom

My hubby said this....

first get the original equation into the form y=mx+b with m being the slope of the line and b being the y intercept. To do this solve the original equation for y. The equation in this form will then look like y=-1/2x+4. When 2 lines are perpendicular the slopes when multiplied together equal -1. Since the slope of your original line is -1/2 the slope of the new line is 2. Then to determine the y intercept of the new line you will use the point which the line passes through (1,-6) and the slope, which was 2. Plug 1 in for x, -6 in for y and 2 in for m in y=mx+b. B with then be equal to -4. Therefore the equation for the new line will be y=2x-4. Then put this equation back into standard form by getting both the x and y terms on the same side of the equation, it will then look like, 2x-y=4.

He said you may wanna double check to see if he screwed up. LOL

[BLEU BOY BARBER]

Im confused I never did understand any of this I hope he gets his answer! I admire him...

[Connie]

Sorry Kristi...I didn't hear back from my son...he must have already gone to bed. It looks like you're getting some help! I hope you all come up with the solution. I stink in Math, so I'm no help!

I've been sick too...on day 8! I hope you and Bryson are better now! *HUG*

[KiKiPie]

Thank yall so much! I can always count on my YT friends to help me!