Question

What is the equation of the trend line? Enter your answers in the boxes. N = M + 45 Scatter plot on a first quadrant coordinate grid. The horizontal axis is labeled Variable M. The vertical axis is labeled Variable N. Points are plotted at (zero, one hundred), (five, one hundred ten), (ten, eighty), (fifteen, fifty), (twenty, seventy), (twenty, one hundred), (twenty-five, sixty), (thirty, twenty), (thirty, seventy-five), (thirty-five, sixty-five), (forty, forty), (forty-five, ten). A line is drawn through (twenty, seventy) and (twenty-five, sixty).

Answer 1

Answer:
`2x+y-110=0`

Explanation:

Given: A line is drawn through (twenty, seventy) and (twenty-five, sixty).

The points through which line is passing are (20,70) and (25,60)

The slope of the line=
`(y_2-y_1)/(x_2-x_1)=(60-70)/(25-20)=(-10)/(5)=-2`

The equation of line with slope m and passing through point
`(x_0,y_0)` is
`(y-y_0)=m(x-x_0)`

Therefore, the equation of the trend line with slope -2 and point (20,70) will be

`(y-70)=-2(x-20)\\\Rightarrow\ y-70=-2x+40\\\Rightarrow\ 2x+y-70-40\\\Rightarrow2x+y-110=0`