How To Convert This Polynomial Equation To Slope Intercept Form To Find X-value From Graph Y =

How to write the slope intercept form of the equation of the line described; (-2,4) parallel to y=3/5x+2?

Given the line y = (3/5)x+2

[parentheses MINE, to remove any possible ambiguity to what I'm answering. The "x" factor is really a part of the numerator of the fraction. If you mean the x to be a factor of the denominator, AS YOU HAVE TYPED IT, then ignore my answer.]

has slope 3/5. Any line parallel to the given line must also have this same slope.

Proposed new parallel line: y = (3/5) x + (b, the y-intercept), but we don't know what b is, YET.

The given point (-2, 4) is supposed to "fit" the new line so...

4 = (3/5) (-2) + b which means b = 4 + 6/5 or 26/5

Your requested parallel line thru (-2, 4) is therefore y = (3/5)x + (26/5).

How to convert this polynomial equation to slope intercept form?

y =−5.1x ² + 34.4x−3.0
Slope intercept form applies to straight line graphs and
this is a quadratic associated with an inverted parabola.

Slope is given by dy/dx = −10.2x + 34.4 (a variable slope)

y axis intercept is given by x = 0 so this is y = -3

Roots, (x-axis intercepts), are given by the quadratic formula
x = [-b ± √(b² - 4ac) ]/2a by substituting
a = −5.1, b =34.4, c= −3

Position of vertex is -b/2a
You can work out the details from this

I hope this is what you need for this question,
Regards - Ian

Change the equation to slope-intercept form.?

Well, there are two ways you can do this.

1) Plot two points on your line and then plug them in to the slope formula. http://www.purplemath.com/modules/slope/slope02.gif This will provide you with the slope.

2) Look at the graph on your calculator. 7/2 graphs a straight horizontal line, right? So the slope is zero. I recommend using the first method though to doublecheck.

How do you convert polynomial quadratic form to vertex form?

You can use a method sometimes called "completing the square." In general, it is as follows:

Suppose you are given a quadratic polynomial f(x) in the form
f(x) = ax^2 + bx + c,
and you want to convert it to the vertex form that you described.

First, factor the a out of the first two terms to give
f(x) = a[ x^2 + (b/a)x ] + c.

Now, inside the set of square parentheses, add and subtract (b/(2a))^2, which still gives the same expression because this is just adding 0:

f(x) = a[ x^2+ (b/a)x + (b/(2a))^2 - (b/(2a))^2 ] + c.

The first three terms inside the square parentheses are now a quadratic polynomial that is a square of a degree 1 polynomial:

f(x) = a[ (x + b/(2a))^2 - (b/(2a))^2 ] + c.

Finally, expand it out by multiplying through the a:

f(x) = a(x + b/(2a))^2 + c - a(b/(2a))^2
= a(x + b/(2a))^2 + c - b^2/(4a),

and it's now in the form that you wanted; it just looks a bit messy because of the general coefficients.

So in general, a polynomial
f(x) = ax^2 + bx + c
in vertex form is
f(x) = a(x + b/(2a))^2 + c - b^2/(4a).

You can work it out manually every time with the method above, or you can just memorize the above formula which will give you the answer very quickly. :)

An example:

Suppose f(x) = 4x^2 + 3x + 7.
Working this out the long way using the method I described:
f(x) = 4x^2 + 3x + 7
= 4[ x^2 + (3/4)x ] + 7
= 4[ x^2 + (3/4)x + (3/(2*4))^2 - (3/(2*4))^2 ] + 7
= 4[ x^2 + (3/4)x + 9/64 - 9/64 ] + 7
= 4[ (x + 3/8)^2 - 9/64 ] + 7
= 4(x+ 3/8)^2 + 7 - 36/64
= 4(x + 3/8)^2 + 103/16.
Or you can use the formula, f(x) = a(x + b/(2a))^2 + c - b^2/(4a), and you get this result almost immediately.

How to convert to slope y intercept form? (y=Mx+b)?

slope intercept form is y=mx+b
m is slope, b is y-intercept.

let's convert -2x - 3y = -7 into slope intercept form.

-2x - 3y = -7

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

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

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

y = -2/3x + 7/3
(the slope is -2/3, y-intercept is 7/3)


if you are still confused, i want you to follow the link below that explains the concept of slope intercept form clearly.
http://www.brightstorm.com/math/algebra/...

How to find x and y intercepts using a Standard Form equation?

To find the y-intercept, you can just convert the standard form equation into slope-y-intercept form.

For example:
y + 2x - 12 = 0 <-- This is in standard form
y = -2x + 12 <-- This is in slope-y-intercept form. Just isolate y and you can tell that the slope is -2, and the y-intercept is 12.

As for the x-intercept, since the definition of an x-intercept is the point on the line where it intersects with the x-axis (or y=0), substitute y with 0.

Back to the example:
0 = -2x + 12
-12 = -2x
x = 6

Therefore, the x-intercept would be 6.

Of course, you could also substitute x=0 to find the y-intercept, but I find using slope-y-intercept form easier.