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

Answer:

2x + 3y = 20

Step-by-step 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:

$y-6=-\frac{2}{3} (x-1)\\\\ 3(y-6)=-2(x-1)\\\\ 3y-18=-2x+2\\\\ 2x+3y=20$

Answer 2

Answer:

2x + 3y = 20

Step-by-step 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.

$6=-\frac{2}{3} (1)+c$

$c=\frac{20}{3}$

So the equation of this line will be:

$y=-\frac{2}{3} x+\frac{20}{3}$

or

2x + 3y = 20