Can someone please help me with finding the slope intercepts and equation for a linear function?
The slope of y = 3 is 0 (because y=3 can be written as y = 0x + 3) Therefore, the slope of this new line must be infinity (meaning it is in the form x = (some number) You said it contains (5, 10) which means 5 is the x - value. An x-line will contain every y value possible while having the same x, so (5,0) (5,15) (5,20) would all be on this line... If 5 is the x value and the slope is infinity, then: x = 5 There is no y- intercept, because to find a y intercept, you solve for (x=0) and that creates an equation without solutions. The x intercept is 5, because to find an x intercept, you solve for (y=0) and your equation still is x= 5. So in conclusion: New line-> x = 5 X intercept-> (5,0) Y intercept-> None
Can someone help me with my math hw. How do i graph y=x using slope and y intercept.?
In order to graph these sorts of functions, you need to understand "slope-intercept form" which follows the formula y=mx+b. y is the value on the y (vertical) axis m is the slope (rise over run, or steepness) of the line x is the value on the x (horizontal) axis b is the point on the y-axis that the line intersects. So, for y=x-2, m=1 (since the coefficient of x is 1) and b=-2. On your graph paper then, you should go to the point (0,-2), which is the y-intercept. Since the slope (m=1) is rise/run (1/1), you should move one unit upward and one unit in the positive x direction. This gives you two points on the line, which is enough to draw the whole thing. For y=-3x+2, your slope is m=-3 and your y-intercept is b=2, or the point (0,2). Just like in the first problem, you should plot the y-intercept point first. From there, use the slope to find the next point. In this case, the slope -3 means you should move 3 units downward and 1 unit in the positive x direction (rise/run is -3/+1). Hope this helps!
Can someone help me solve this,I need to find the y-intercept and slope for these two : x+y=21, 5x+10y=175?
equation: x + y = 21 first put it in y-intercept form: y = -x + 21 y-intercept is what y equals when x=0, so: y = -(0) + 21 y = 21 the slope is the coefficient for x when the equation is in y-intercept form, so: y = -x + 21 slope = -1 ------------------------------- equation: 5x + 10y = 175 put it in slope-intercept form: 5(x + 2y) = 5(35) factor out the five x + 2y = 35 y = (-x + 35)/2 slope-intercept therefore is: y = (-(0) + 35)/2 = 35/2 slope therefore is: y = (-x + 35)/2 coeff. of x: -1/2 --------------------------------- just remember this trick: slope-intercept for will give you both the things you need. the slope-intercept form is: y = mx + b if you can get it into that form, all the information will stand out for you. y and x will be variables (there won't be numbers there, just y and x) and... m = slope b = y-intercept
How do I find the equation that is perpendicular to the line 7x - 2y = 8 and intersects the line 7x - 2y = 8 at x = 8?
We first need to get the equation of the desired straight line in the point-slope form: y – y1 = m(x – x1), and then put it in the general form of Ax + By = - C.Since the equation of line that we’re looking for is perpendicular to the given line 7x – 2y = 8, then the slope m2 of the line that we’re looking for is the negative reciprocal of the slope m1 of the given line 7x -2y = 8, i.e., m2 = - (1/m1).Now, finding the slope of the given line 7x - 2y =8 as follows:-2y = -7x + 8, then, solving for y, we get: y = (7/2)x – 4; therefore, the slope of our desired line is m2 = - (1/m1) = - (1/7/2) = -2/7.Since the given line intersects our desired line at x = 8, we know that the two lines have a point in common, and solving for the y-coordinate of the point of intersection, we get:7(8) – 2y = 856 – 2y = 8-2y = -56 + 8-2y = -48y = 24, therefore, substituting, our desired line has the following equation:y – 24 = (-2/7)(x – 8)y – 24 = (-2/7)x + (16/7)7y – 168 = -2x + 162x + 7y = 184 is our desired line.
Finding the slope of f(x)= -6x-3
the slope is -6, and the y-intercept is -3, the equation said f(x)= -6x-3, the number that is attatched to the variable by multiplication ( -6x in this situation) is the slope, so the slope is -6. Y-intercept is (0,-3), this point is where the graph crosses the y-axis, so on a graph you start at 0 and go down 3 space, and -3 is the y-intercept, so the graph will cross the y-axis at (0,-3). hope this helps.
Quadratics help? Thanks!?
1. Use the Completing the Square method to find the vertex form of the quadratic function y = 2x^2 + 8x + 18. 2. In the question, use the information s(t) = -16t^2 + v0t + s0 We throw a rock into the air with initial velocity of 50 ft/sec, and initial position of 6 ft. Find how high the rock goes before coming back down. To answer this question, fill in the blanks in the following sentence, where the first blank gives this height, and the second blank gives how many seconds into the flight of the rock it reaches this maximum height. The rock reaches its highest position of _______ feet above the ground after _______ seconds of flight These are some select problems that I'm not sure about out of a bunch that I get from the math from random worksheets I downloaded to teach myself Alg 2 over the summer. I numbered them for the convenience of answering. Quadratics are odd. If anyone can solve all of them it would be great, because I learn best from seeing it done... Thanks again!
How do you find the equation of a trend line?
A trend line is sought when one is dealing with two-dimensional data, i.e. [math](x,y) [/math]points. It then depends on whether you consider that the [math]x[/math] data is error-free, or if both [math]x[/math] and [math]y[/math] could be altered by errors.If [math]x[/math] is error-free, one will minimizes the sum of the squares of the differences between your data [math]y_i[/math] and its estimation from the trend line [math]ax_i+b[/math], i.e. minimizes[math]S(a,b)=\sum_i (ax_i+b-y_i)^2[/math]To do so, one takes both derivatives [math]\partial S/\partial a[/math] and [math]\partial S/\partial b[/math] to be [math]0[/math].[math]\frac{\partial S}{\partial a}=2\sum_i x_i(ax_i+b-y_i)=0[/math][math]\frac{\partial S}{\partial b}=2\sum_i ax_i+b-y_i=0[/math]From which one gets the system of equations ([math]\langle x^2\rangle[/math] is the mean value of the [math]x_i^2[/math]s, [math]\langle xy\rangle[/math] that of the products [math]x_iy_i[/math]…)[math]\begin{align}a\langle x^2\rangle+b\langle x\rangle&=\langle xy\rangle\\a\langle x\rangle+b&=\langle y\rangle\end{align}[/math]the solution of which is[math]a=\frac{\langle xy\rangle-\langle x\rangle\langle y\rangle}{\langle x^2\rangle-\langle x\rangle^2}[/math][math]b =\frac{\langle y\rangle\langle x^2\rangle-\langle x\rangle\langle xy\rangle}{\langle x^2\rangle-\langle x\rangle^2}[/math]which leads to[math]y=\frac{\langle xy\rangle-\langle x\rangle\langle y\rangle}{\langle x^2\rangle-\langle x\rangle^2}(x-\langle x\rangle)+\langle y\rangle[/math]Somewhat more involved is the case of both x and y subjects to errors; how could one find the proper trend line? An answer is to minimize the sum of the distances between the points and the line, or the sum of the squares of these distances.The latter being easier to deal with analytically, it will be my choice: the equation of the trend line is [math]x\sin\theta-y\cos\theta+d=0[/math], and one wants to minimize (the quantity between parenthesis is the distance from the line to the point [math](x_i,y_i)[/math]):[math]S=\sum_i (x_i\sin\theta-y_i\cos\theta+d)^2[/math]playing the same game as previously, one sets the two partial derivatives to [math]0[/math], to find the equation of the trend line:[math]y=\tan\theta(x-\langle x\rangle)+\langle y\rangle[/math]where [math]\theta[/math] is given by[math]\tan2\theta=2\frac{\langle xy\rangle-\langle x\rangle\langle y\rangle}{\langle x^2\rangle-\langle x\rangle^2-\langle y^2\rangle+\langle y\rangle^2}[/math]
What is the equation of the line perpendicular to x+7y=8, and passes through the points (-4,-42)? Please show a method
Perpendicular to a line means the negative reciprocal of the slope. So first, let's find the slope of [math]x+7y=8[/math]. To do that, we need to rearrange it to slope intercept form ([math]y=mx+b[/math]).[math]x+7y=8[/math][math]x+7y-8=0[/math][math]x-8=-7y[/math][math]\frac{1}{-7}x-\frac{8}{-7}=y[/math][math]y=-\frac{1}{7}x+\frac{8}{7}[/math][math]m=-\frac{1}{7}[/math]Negative reciprocal of [math]-\frac{1}{7}[/math] is [math]7[/math]. So the perpendicular line has a slope of 7. And, we can begin to create the equation for the perpendicular line: [math]y=7x+b[/math].Using the information in the original problem, we can find the value of the y-intercept, b. The line must pass through (-4, 42). Simply plug those values into [math]y=7x+b[/math] and solve for b.[math]-42=7(-4)+b[/math][math]-42=-28+b[/math][math]-42+28=b[/math][math]-14=b[/math]So now our equation becomes [math]y=7x-14[/math]
Graphing the line....?
The coordinates for the points are given in (x,y) order. You just plot the two points and draw a line passing through both of them and extending out both directions. A. Slope is Rise/Run or (Change in Y)/(Change in X) or sometimes written as (Y2-Y1)/(X2-X1) so you subtract one of the Y's from the other and in the same order subtract one of the X's from the other... Y2 - Y1 (-1) - (-2) = -1 + 2 = 1 (using the first point as (X2, Y2)) (-2) - (-1) = -2 + 1 = -1(using the first point as (X1, Y1)) X2 - X1 7 - 3 = 4 (using the first point as (X2, Y2)) 3 - 7 = -4 (using the first point as (X1, Y1)0 (Y2 - Y1) / (X2 - X1) 1 / 4 (slope using the first point as (X2, Y2)) -1/-4 = 1/4 (slope using the first point as (X1, Y1)) notice that the slope came out the same with either calculation.. a positive slope means that the line goes up as it goes from left to right.. and it goes up 1 for every 4 that it goes across. y = mx + b is the slope intercept form of an equation where x is the independent variable (on the horizontal axis), y is the dependent variable (on the virtical axis), m is the slope and b is the value of y when x = 0 (y-intercept) plug in known values for one of the points y = (1/4)x + b (slope = 1/4 but we don't know b yet.. so solve for it... -1 = (1/4)7 + b (put in values of x and y from first point) -1 = 7/4 + b -1 - (7/4) = b -(4/4) - (7/4) = b -(11/4) = b a. slope = 1/4 b. y-intercept = -11/4 c. slope intercept equation: y = (1/4)x - 11/4 *** sorry Hellokitty.. your link does not work
Given a set dataset of (x,y) coordinates, how can I determine the equation of find a line non-linear function that contains all of those coordinatespasses through each point?
you can use wolfram alpha at least to get started. here are a bunch of different variants: http://www.wolframalpha.com/inpu...http://www.wolframalpha.com/inpu...http://www.wolframalpha.com/inpu...it will usually spit out the function(s) for the curve(s) at the very top and some plots below. the first link is an actual interpolation (all points are on the curve) while the second and third link contain approximations (points are very close to the resulting curve). when you look at the examples also check for the 'related questions' box to the right of the results, it usually contains other interesting queries.