Answer:
Thus, 7x + 10y = 3 is not a good model because the given point will not pass through the given straight line.
Step-by-step explanation:
We are given the following information in the question:
The two points (8,5) and (-12,-9) lies on a straight line.
We can find the equation of this straight line with the help of two point form equation of line. It says:
[tex]y - y_1 = \displaystyle\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Putting [tex](x_1,y_1) = (8,5), (x_2,y_2) = (-12,-9)[/tex]
we have:
[tex]y-5 = \displaystyle\frac{-9-5}{-12-8}(x-8)\\\\\Rightarrow y - 5= \frac{-14}{-20}(x-8)\\\\\Rightarrow 10(y-5) = 7(x-8)\\\Rightarrow 10y-50 = 7x - 56\\\Rightarrow 56-50 = 7x -10y\\\Rightarrow 7x-10y = 6[/tex]
This the equation of straight line passing through the given points.
Thus, 7x + 10y = 3 is not a good model because the given point will not pass through the given straight line.
Answer:
If the model is good, then both points will check in the equation. Substituting 8 for x and 5 for y in the equation results in 56 – 50 = 3, which is not true. Therefore, the model is not good. Using (–12, –9) as a check results in –84 + 90 = 3. The constant value in the equation should be 6, not 3. In slope-intercept form, the y-intercept should be –3/5.
Step-by-step explanation:
