equations etc.

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candy101

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find an equation of the line through (-4,3) which is perpendicular to the line 2x-3y+7
{can you please explain the steps that i have to take or give me a website that does}

(just in general how do i find an equation of a line that is perpendicular to another line) :!:


and how do i sketch y=2x^2+12x-14 and indicate its vertex and all intercepts ( in general how should i go about solving problems like this and please let me know the steps i have to take)


Thanks
 
candy101 said:
find an equation of the line through (-4,3) which is perpendicular to the line

2x-3y+7 ? Is the plus sign in this expression supposed to be an equals sign?

A line is given by an equation; not an expression. Please double-check your typing.

{can you please explain the steps that i have to take or give me a website that does}

(1) Find the slope of the given line

(2) Determine the negative reciprocal of this slope

(3) Use the negative reciprocal as the slope of the perpendicular line

(4) Use the Point-Slope formula to write the perpendicular line's equation

(just in general how do i find an equation of a line that is perpendicular to another line) :!: In general, it depends upon what information you've been given.


and how do i sketch y=2x^2+12x-14 and indicate its vertex and all intercepts ( in general how should i go about solving problems like this and please let me know the steps i have to take)

Learn how to work with linear equations first; then you'll be ready to start working with quadratic equations.
Thanks
Click to expand...
 
>>>find an equation of the line through (-4,3) which is perpendicular to the line 2x-3y+7.

Perpendicular lines have slopes that are negative reciprocals of each other. For instance, if the slope of line l is 4, then the slope of a line perpendicular to l is -1/4. Regarding your problem. First, find the slope of 2x-3y+7=0 (I guess that's what you mean although you left off the "=0") and call it m. The slope of the desired line will be -1/m. Next, you might use the point-slope form for the equation of a line, namely y-y[sub:1nupzil8]1[/sub:1nupzil8] = m(x-x[sub:1nupzil8]1[/sub:1nupzil8]). The slope is m that you just found. The given point (-4,3) is (x[sub:1nupzil8]1[/sub:1nupzil8],y[sub:1nupzil8]1[/sub:1nupzil8]). So plug -4 in place of x[sub:1nupzil8]1[/sub:1nupzil8] and 3 in place of y[sub:1nupzil8]1[/sub:1nupzil8]. simplify it and put it into the desired form.
 
candy101 said:
… the equation is 2x - 3y = 7
Click to expand...


Okay. Did you try any of the steps that I listed?

Let's start with step (1).

Do you know how to find the slope of the line given by the equation above?

 
so the equation is 2x-3y=7

just wanna make sure i'm on the right track

first i found the slope

i took 2x-3y=7 i took the 2x and move it over making it


2x/2x-3y=7/2x
so the 2x cancel out so i'm left with

-3y=-2x+7?
then i divide -3
-3y/-3=2x/-3+7/-3
and i got as an final ans. y=-2/3x+7/3
-2/3 is the slope and 7/3 is the intercept??

is this right? if not what did i do wrong?
after i find out if this step is right then i will move on to the next


thanks guys for the help
P.S Im sorry for the error
 
candy101 said:
so the equation is 2x - 3y = 7

just wanna make sure i'm on the right track

i took 2x-3y=7 i took the 2x and move it over making it

2x/2x-3y=7/2x ? I hope these slashes are typographical errors. We are subtracting 2x from both sides.

2x - 2x - 3y = 7 - 2x

so the 2x cancel out

-3y = -2x + 7

then i divide [by] -3

-3y/-3 = 2x/-3 + 7/-3 ? You dropped the negative sign on -2

-3y/(-3) = -2x/(-3) + 7/(-3)

and i got as an final ans. y = -2/3x + 7/3 ? Dividing 7 by -3 gives -7/3.

After correcting your sign errors, the Slope-Intercept form is:

y = (2/3)x - 7/3

-2/3 is the slope and 7/3 is the intercept??

The slope of the given line is 2/3, and we don't care where the line crosses the y-axis. The first step is to find the given line's slope only.

after i find out if this step is right then i will move on to the next Good.

The next step is to calculate the negative reciprocal of 2/3 because slopes of perpendicular lines are negative reciprocals of each other.

Once we know the slope of the perpendicular line, then we can use it and the given point through which the line passes to write the equation.

Are you familiar with the Point-Slope formula?

I'll wait to see.
Click to expand...
 
ok so i did

y-y1=m (x-x1)

y-3= -3/2 (x-(-4))
then

y-3=-3/2x + 6

Then i add 3 to both side : canceling out the -3 and adding 3 to 6

so i got this as a final ans: y=-3/2x + 9 ?????

is this right :?:

thank you guys for the awesome help!! i am so grateful!!! :D
 
candy101 said:
y - 3 = -3/2x + 6

(-3/2)(4) = -6, not 6.

One of your difficulties in this discussion seems to be that you are not paying attention to negative signs.

Then i add 3 to both side : canceling out the -3 and adding 3 to [-6]

The equation of the line perpendicular to the line 2x - 3y = 7 passing through the point (-4, 3) is:

y = (-3/2)x - 3
Click to expand...


Actually, since the instructions state to find "an equation", we are not required to put the equation into Slope-Intercept form.

The Point-Slope form is just as valid, as are any of the other four forms of a line's equation.

y - 3 = -(3/2)(x + 4)

 
oh! i c i where i went wrong! thanks so much!!

can u help me with the second one? what are the needed steps?
{and do u know of any sites where i can get practice questions on my first question}
 


Have you ever used the Google search engine to find stuff on the Internet?

Googling keywords "perpendicular lines worksheet" lists many resources, including THIS ONE.

The second exercise involves a quadratic equation of the form

y = ax^2 + bx + c

The shape of the graph of a quadratic equation is called a parabola.

The intercepts are points where the graph crosses the axes. All parabolas cross the y-axis, but not all parabolas cross the x-axis, and some parabolas touch the x-axis at a single point only.

To find the y-intercept, replace x with 0 and calculate y.

To find the x-intercepts, replace y with 0 and solve for x.

The formula for determining the x-coordinate of the vertex is -b/(2a).

Once you have the value of x at the vertex, use the equation to find the corresponding y-coordinate of the vertex.

Make a table of other xy-coordinates on the parabola by picking some whole numbers for x and calculating their corresponding y values.

Are you taking a math class? Do you have a textbook?

 
yea i do have math ..my math book didn't come yet (internet order)

how would i know when i have a question containing a parabola?


Thanks a bunch!!!!!!!!!!!! :D
 
candy101 said:
how would i know when i have a question containing a parabola?
Click to expand...


As soon as you're given an equation of the form y = a*x^2 + b*x + c, or as soon as you form such an equation from given information, you have a situation where the graph is a parabola.

 
convert degree to radius

thanks


i got this other problem i kind of know how to do it but im not that sure

convert 144 degree to radius
this is what the teacher did

x/144degree =pie/180degree

and then cross multiply

then he got

180x/180=144pie/180

and the answer is x= 12pie/15 = 4pie/5

i wanna know how he got the answer?
when i divided 144 by 180 i didn't get that answer ..i got 0.8
did he like use the greatest common factor?
so im kind of lost there
 
144/180 = 4/5 = .8 ; so both 4/5 and .8 are correct.

By the way, you should have started a NEW thread for this NEW problem.
 
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