Question

Line n passes through the points (-3,-7.5) and (2,-5). Thalia determined that the equation of the line n is y=0.5x. Explain the error Tahlia paid while determining her equation .be sure to include the correct equation in your explanation

Answer 1

The error is -6

Explanation:

If a line passes through the points
`(x_1,y_1)` and
`(x_2,y_2)`

Then the equation of line is

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

Here given points are (-3,-7.5) and (2,-5)

Then the equation of the line is

`(x+3)/(-3-2) =(y+7.5)/(-7.5+5)`

⇔
`(x+3)/(-5) =(y+7.5)/(-2.5)`

⇔2.5(x+3) = 5(y+7.5)

⇔(x+3)= 2(y+7.5)

⇔x+ 3 = 2y +15

⇔2y = x+3-15

⇔y =
`(x-12)/(2)`

⇔y = 0.5 x -6

The error is -6