devon wants to write an equation for a line that passes through 2 of the data points he has collected. the…

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.

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

Answer:

No, it is not a good model.

Explanation:

Step1: Find slope between points

The slope $m$ between two points $(x_1,y_1)=(8,5)$ and $(x_2,y_2)=(- 12,-9)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-9 - 5}{-12 - 8}=\frac{-14}{-20}=\frac{7}{10}$.

Step2: Use point - slope form

Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(8,5)$ and $m = \frac{7}{10}$, we have $y - 5=\frac{7}{10}(x - 8)$.

Step3: Convert to standard form

$y-5=\frac{7}{10}x-\frac{56}{10}$, multiply through by 10: $10y-50 = 7x-56$, which simplifies to $7x-10y=6$. Since the equation Devon wrote is $7x - 10y=3$ and the correct equation for the line through the two points is $7x - 10y=6$, his equation is not a good model for the line passing through the given points.