To find the equation of a line given a point and the slope of the line, we can use the point-slope formula, which is defined below:
[tex](y - y_1) = m(x - x_1)[/tex]
([tex]m[/tex] is the slope of the line and ([tex]x_1[/tex], [tex]y_1[/tex]) is a point on the line)
Using the formula, we can find the equation of the line:
[tex](y + 2) = \dfrac{1}{3}(x - 1)[/tex]
[tex](y + 2) = \dfrac{1}{3}x - \dfrac{1}{3}[/tex]
[tex]y = \dfrac{1}{3}x - \dfrac{7}{3}[/tex]
However, we need to convert this equation into standard form. First, let's try to remove all of the fractions within the equation. To do this, we can multiply by the GCD of the fractions, which in this case is 3:
[tex]3y = x - 7[/tex]
Now, we can move terms around to form the true standard form (Ax + By = C):
[tex]3y = x - 7[/tex]
[tex]3y - x = -7[/tex]
[tex]x - 3y = 7[/tex]
The equation of the line is x - 3y = 7.
