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

Step-by-step explanation:

Given: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.

To find:Is this a good model? Explain your reasoning.

Solution:

If a line passes through two points A(x1,y1) and B(x2,y2)

then equation of line is given by

$\boxed{\bold{\red{(y - y_2) = \frac{y_2 - y_1}{x_2 - x_1} (x - x_2)}}}$

Here,

A(8,5) and B(-12,-9)

Equation of line is

$[y -( - 9) ] = \frac{ - 9 - 5}{ - 12 - 8} [x - ( - 12)] \\ \\ y + 9 = \frac{ - 14}{ - 20} (x + 12) \\ \\ y + 9 = \frac{7}{10} (x + 12) \\ \\ 10y + 90 = 7x + 84 \\ \\ - 7x + 10y + 90 - 84 = 0 \\ \\ - 7x + 10y + 6 = 0 \\ \\ \bold{\green{7x - 10y = 6} }$

This is equation of line 7x - 10y = 6 passing through two points (8, 5) and (–12, –9).

The line written by Devon is actually parallel to line which passes through (8, 5) and (–12, –9).

Hope it helps you.

To learn more on brainly:

1)63. Given points A(1,5), B(-3, 7) and C(15,9).

(1) Find the equation of a line passing through the mid-point of AC and t...

https://brainly.in/question/12355170

2)write the equation of the line passing through the point 3, 5 and a parallel to the x axis

https://brainly.in/question/11695662

Answer 2

Answer:

This is equation of line 7x - 10y = 6 passing through two points (8, 5) and (–12, –9).

This is equation of line 7x - 10y = 6 passing through two points (8, 5) and (–12, –9).The line written by Devon is actually parallel to line which passes through (8, 5) and (–12, –9).