Example Question - intersection point
Here are examples of questions we've helped users solve.
Solving System of Linear Equations by Graphing
The image shows a screenshot of a math homework problem asking to solve the system of linear equations by graphing: 1) y = x - 7 2) y = 2x - 2 To graph these equations, you need to plot at least two points for each line and then draw a straight line through these points. For the first equation, y = x - 7: - When x = 0, y = -7. The point is (0, -7). - When x = 7, y = 0. The point is (7, 0). Plot these two points and draw a line through them. For the second equation, y = 2x - 2: - When x = 0, y = -2. The point is (0, -2). - When x = 1, y = 0. The point is (1, 0). Plot these two points as well and draw a line through them. The solution to the system of equations is the point where the two lines intersect. By examining the graph that would be created, you can visually determine the point of intersection and that will be the solution to the system of equations. In the provided image, there is a small section of the graph visible, but to be precise, you would need to plot these points on a full graph, either on paper or using graphing software. The system's solution will be the coordinates where both lines cross each other on the graph. The exact solution can be found by setting the two equations equal to each other and solving for x, then using that x-value to find the corresponding y-value. However, since the task specifically asks to use the graphing tool, the solution should be obtained graphically.
Determining Number of Solutions for a System of Equations from Intersection Point on a Graph
The image provided shows a graph on a rectangular coordinate system with two lines that intersect. The question asks to determine the number of solutions for the system of equations represented by these lines. If two lines intersect on a graph, it means they have exactly one point in common, which signifies there is exactly one solution to the system of equations. The coordinates of that solution are located at the intersection point. However, due to the low resolution of the image, I'm not able to clearly see the intersection point's coordinates. Normally, to answer this question, I would identify the exact point where the two lines intersect and provide those coordinates, which would represent the solution to the system of equations. Since the question prompts to give the coordinates if there is only one solution, you should look on the graph for where the two lines cross, and provide the x and y values of that point. It's also worth mentioning the other possible answer choices in the question: - "The only solution is ________________." (the blank would normally be filled with the coordinates of the intersection point) - "There is no solution." - "There is an infinite number of solutions." Given that the lines intersect, the correct answer is not "There is no solution" nor "There is an infinite number of solutions," but the first option, specifying the coordinates of the intersection point. Since I cannot provide the coordinates due to the image's quality, you can visually estimate or determine them using the provided graph in the image. If you need help with that, please provide a clearer image or the coordinates of points close to the intersection.
Calculating Intersection Point of Diagonals in Rectangle
在這個問題中，我們需要確定矩形PQRS中對角線PT和QS的交點T的長度TS。 首先，我們可以觀察到，因為PQRS是矩形，所以對角線PS和QT將等長且交於中點。由此，TS將是PS的一半。 要找出PS的長度，我們可以使用畢氏定理，因為PQ和QR是矩形的兩個直角邊: \(PS^2 = PQ^2 + QR^2\) 代入已知的長度: \(PS^2 = 24^2 + 12^2 = 576 + 144 = 720\) 然後，開平方根計算PS: \(PS = \sqrt{720}\) 這給了我們PS的長度。為了獲得TS，我們只需將結果除以2： \(TS = \frac{PS}{2} = \frac{\sqrt{720}}{2}\) 現在來計算它的確切值: \(PS = \sqrt{720} \approx 26.83 \, \text{cm}\) (保留兩位小數) 所以, \(TS = \frac{26.83}{2} \approx 13.42 \, \text{cm}\) (保留兩位小數) 所以TS的長度大約是13.42厘米。
Finding the Intersection Point of Two Lines
To find the point at which the two lines represented by the equations intersect, you can utilize the method of substitution or elimination. In this case, substitution seems straightforward as the first equation is already solved for y. Here is how you do it: You have the following two equations: 1) \( y = 2x - 8 \) 2) \( x + y = 19 \) Substitute the expression from the first equation for y in the second equation: \( x + (2x - 8) = 19 \) Combine like terms: \( 3x - 8 = 19 \) Add 8 to both sides to isolate the term with \( x \): \( 3x = 27 \) Divide by 3 to solve for \( x \): \( x = 9 \) Now that we have the value of \( x \), we can plug it back into the first equation to find the corresponding value of \( y \): \( y = 2(9) - 8 \) \( y = 18 - 8 \) \( y = 10 \) Therefore, the point of intersection for the two lines is at the coordinates (9, 10).
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