Question

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 1

Use slope formula to find slope −9−5−/12−8=−14/−20=7/10 7/10 = m = slope  
y= mx + b
y= (7/10)x + b
(8,5)
(5) = (7/10)(8) + b
b = -3/5

So.... y=(7/10)x −35

multiply by 10

10y=7x−6 --> -7x + 10y = -6
 --> 7x - 10y = 6
 So, if 7x - 10y = 3 a good model?

Answer 2

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. Hope this helps!!! :)