Question

Which equations correctly represent a line that has a slope of -2/3 and passes through the points (–2, 8) and (1, 6)?

Answer 1

2x + 3y = 20

Explanation:

We are given two points: (–2, 8) and (1, 6) and the slope (m) of the line and we are to find the equation of this line.

We know that the standard equation of a line is:

`y=mx+c`

So we will plug in the given values in the above equation to find the y intercept.

`6=-(2)/(3) (1)+c`

`c=(20)/(3)`

So the equation of this line will be:

`y=-(2)/(3) x+(20)/(3)`

or

2x + 3y = 20

Answer 2

2x + 3y = 20

Explanation:

Slope of the line is -2/3 . We can use any of the given points to find the equation of the line. Lets use (1, 6)

The general point-slope form of a line is:

`y-y_(1) =m(x-x_(1) )`

Here m is the slope which is -2/3

x1 and y1 are the coordinates of the point. So x1 = 1 and y1 = 6

Using these values, we get:

`y-6=-(2)/(3) (x-1)\\\\ 3(y-6)=-2(x-1)\\\\ 3y-18=-2x+2\\\\ 2x+3y=20`