Devon wants to write an equation for a line that passes through 2 of the data points he has collected. The points are $(8,5)$ and $(-12,-9)$. He writes the equation $7x - 10y = 3$. Is this a good model? Explain your reasoning.

Question

Anonymous · Answer

The equation 7 x − 10 y = 3 is not a good model for the points ( 8 , 5 ) and ( − 12 , − 9 ) because neither point satisfies the equation. Substituting both points yields a result of 6 instead of 3. Therefore, the equation does not represent the relationship between these data points correctly. 
 ;

GinnyAnswer · Answer

Substitute the point ( 8 , 5 ) into the equation 7 x − 10 y = 3 and get 7 ( 8 ) − 10 ( 5 ) = 6 , which is not equal to 3. 
 Substitute the point ( − 12 , − 9 ) into the equation 7 x − 10 y = 3 and get 7 ( − 12 ) − 10 ( − 9 ) = 6 , which is not equal to 3. 
 Since neither point satisfies the equation, the equation is not a good model. 
 The equation is not a good model: No ​ 
 
 Explanation 
 
 Problem Analysis We need to determine if the equation 7 x − 10 y = 3 is a good model for the points ( 8 , 5 ) and ( − 12 , − 9 ) . To do this, we will substitute each point into the equation and see if the equation holds true. 
 
 Checking Point (8, 5) First, let's check the point ( 8 , 5 ) . We substitute x = 8 and y = 5 into the equation 7 x − 10 y = 3 :
 7 ( 8 ) − 10 ( 5 ) = 56 − 50 = 6 Since 6 e q 3 , the point ( 8 , 5 ) does not satisfy the equation. 
 
 Checking Point (-12, -9) Next, let's check the point ( − 12 , − 9 ) . We substitute x = − 12 and y = − 9 into the equation 7 x − 10 y = 3 :
 7 ( − 12 ) − 10 ( − 9 ) = − 84 + 90 = 6 Since 6 e q 3 , the point ( − 12 , − 9 ) does not satisfy the equation either. 
 
 Conclusion Since neither of the points ( 8 , 5 ) and ( − 12 , − 9 ) satisfy the equation 7 x − 10 y = 3 , the equation is not a good model for the given data points.

Examples 
 In data analysis, it's crucial to validate models against known data points. For instance, if you're predicting sales based on marketing spend, you'd check if your model accurately reflects past sales data. If the model deviates significantly from actual data, like in this problem, it indicates the model needs refinement or a different approach altogether. This ensures that predictions are reliable and useful for decision-making.

Devon wants to write an equation for a line that passes through 2 of the data points he has collected. The points are $(8,5)$ and $(-12,-9)$. He writes the equation $7x - 10y = 3$. Is this a good model? Explain your reasoning.

Answer (2)

Related Questions in Mathematics

📝 Answered - Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

📝 Answered - Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

📝 Answered - What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

📝 Answered - The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

📝 Answered - If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]