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

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.

Explanation:

Answer 2

Thus, 7x + 10y = 3 is not a good model because the given point will not pass through the given straight line.

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:

`y - y_1 = \displaystyle(y_2-y_1)/(x_2-x_1)(x-x_1)`

Putting
`(x_1,y_1) = (8,5), (x_2,y_2) = (-12,-9)`

we have:

`y-5 = \displaystyle(-9-5)/(-12-8)(x-8)\\\\\Rightarrow y - 5= (-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`

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.