what is an equation of the line that passes through the points (3, 0) and (-6, -3)?

Explanation:

Step1: Calculate the slope

The slope ( m ) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Here, ((x_1,y_1)=(3,0)) and ((x_2,y_2)=(-6,-3)). So, ( m=\frac{-3 - 0}{-6 - 3}=\frac{-3}{-9}=\frac{1}{3} ).

Step2: Use point - slope form

The point - slope form of a line is ( y - y_1=m(x - x_1) ). Using the point ((3,0)) and ( m = \frac{1}{3} ), we have ( y - 0=\frac{1}{3}(x - 3) ).

Step3: Simplify the equation

Simplify ( y=\frac{1}{3}x - 1 ), or we can write it in standard form ( x - 3y=3 ).

Answer:

The equation of the line is ( y=\frac{1}{3}x - 1 ) (or ( x - 3y = 3 ))