Step-by-step explanation:
The point-slpe form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁, y₁), (x₂, y₂) - points on a line
We have the points (3, 0) and (-3, -6).
Calculate the slope:
[tex]m=\dfrac{-6-0}{-3-3}=\dfrac{-6}{-6}=1[/tex]
Put the value of the slope and the coordinates of the point (3, 0) or (03, 06) to the equation of a line:
FOR (3, 0):
[tex]y-0=1(x-3)\to y=1(x-3)\to y=x-3[/tex]
FOR (-3, -6):
[tex]y-(-6)=1(x-(-3))\to y+6=1(x+3)\to y+6=x+3[/tex]
