Question

What is the equation of the line that passes through the points (−2, 3) and (2, 7)?

x − y = −1
x − y = −2
x − y = − 5
x − y = − 6

Answer 1

The point-slope form of line:

`y-y_1=m(x-x_1)`

The fomula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

Substitute the coordinates of the points:

`m=(7-3)/(2-(-2))=(4)/(2+2)=(4)/(4)=1\\\\y-7=1(x-2)`

`y-7=x-2` subtract y from both sides

`-7=x-y-2` add 2 to both sides

`-5=x-y\to\boxed{x-y=-5}`