Question

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

Answer 1

The point-slope form of line:

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

The fomula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute the coordinates of the points:

$m=\dfrac{7-3}{2-(-2)}=\dfrac{4}{2+2}=\dfrac{4}{4}=1\\\\y-7=1(x-2)$

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

$-7=x-y-2$     add 2 to both sides

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