Determien the resulting function of the line with points (1,2) and (3,3) and

In summary, the conversation discusses finding the resulting function of a line with points (1,2) and (3,3) and f(x) = 2x^2 + 9 and determining its intersection. The correct equation for the line is y = 1/2x + 3/2, but the quadratic equation that was derived is incorrect and does not intersect the x-axis. There is a suggestion to check the algebra and consider the possibility that there may not be an intersection.
  • #1
cruisx
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Determien the resulting function of the line with points (1,2) and (3,3) and...

Homework Statement




hi guys how are you, i am having a little trouble solving the question adn was wondering if some of you could give me a hand?

Determine the resulting function of the line with points (1,2) and (3,3) and f(x) = 2x^2 + 9 intersect?

Homework Equations





The Attempt at a Solution



Now idk how to solve this as its been a while since i did any math but i tried to put it into an equation of a line and i got y=1/2x+3/2 but i know that's not right as its for an equation of a line =/. I know i need to use the two points to make an equation and then do this

equation = 2x^2 + 9 but i don't know how to solve the two points and get an equation.
 
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  • #2


Sorry if I'm being obtuse, but are trying to find the intersection between the line with points (1,2) and (3,3) and the function f(x) = 2x2 + 9? If so, you've gotten the equation for the line correct, now all you would need to do is solve for the intersections. If I've misinterpretted the question, hopefully you wouldn't mind clarifying for me.
 
  • #3


I am trying to find the intersection so i guess i am right. So i woudl do this right?

1/2x + 3/2 = 2x^2 + 9

and that would result to

-2x2 + 1/2x + 21/2 = 0

Is this correct? Also could you see if this is correct as well?

I am given a y-intercept of 0 and a point of (2,2) and the equation of the line i got is this

y = 1x + 0

is that correct?
 
Last edited:
  • #4


Well, your new quadratic equation isn't quite right (check the algebra)! The equation that you should get never intersects the x-axis. What does this suggest?
 
  • #5


why not? what's wrong with it? which one are u referring too?
 
  • #6


ohh i think you are right, should it be - 22 + 1/2x - 15/2 ??
 

1. What is the equation of the line with points (1,2) and (3,3)?

The equation of a line can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. To find the equation of the line with points (1,2) and (3,3), we first need to calculate the slope using the formula (y2 - y1)/(x2 - x1). In this case, the slope is (3-2)/(3-1) = 1/2. Next, we can substitute the slope into the equation y = mx + b, along with one of the given points. Using (1,2), we get 2 = (1/2)(1) + b. Solving for b, we get b = 3/2. Therefore, the equation of the line is y = (1/2)x + 3/2.

2. How do you plot a line with points (1,2) and (3,3)?

To plot a line with points (1,2) and (3,3), we first need to draw a coordinate plane with labeled x and y axes. Then, we can plot the two points on the plane by finding their corresponding coordinates and marking them on the axes. In this case, point (1,2) would be plotted one unit to the right on the x-axis and two units up on the y-axis. Point (3,3) would be plotted three units to the right on the x-axis and three units up on the y-axis. Once both points are plotted, we can draw a straight line through them to represent the line with these points.

3. How do you find the slope of a line with points (1,2) and (3,3)?

To find the slope of a line with points (1,2) and (3,3), we can use the formula (y2 - y1)/(x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. In this case, we would substitute (1,2) for (x1,y1) and (3,3) for (x2,y2) to get (3-2)/(3-1) = 1/2. Therefore, the slope of the line is 1/2.

4. What is the significance of finding the equation of a line with two points?

Finding the equation of a line with two points allows us to represent the relationship between those points in a mathematical form. This can be useful in various applications, such as predicting future values, analyzing trends, and solving real-world problems. It also allows us to easily graph the line and make calculations, such as finding the slope and y-intercept.

5. Can the equation of a line with two points be used to determine the slope of the line at any given point?

Yes, the equation of a line with two points can be used to determine the slope of the line at any given point. This is because the slope of a line is constant throughout the entire line. So, if we know the equation of the line, we can plug in the x-coordinate of a specific point to find the slope at that point.

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