The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))(y−y1)=m(x−x1)
Where color(blue)(m)m is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
Substituting the values from the point and the slope given in the problems allows us to write this equation:
(y - color(red)(-2)) = color(blue)(1/3)(x - color(red)(3))
(y + color(red)(2)) = color(blue)(1/3)(x - color(red)(3))
We can also transform this to the slope-intercept form by solving for y. The slope-intercept form of a linear equation is: y = color(red)(m)x + color(blue)(b)
Where color(red)(m) is the slope and color(blue)(b) is the y-intercept value.
y + color(red)(2) = (color(blue)(1/3) xx x) - (color(blue)(1/3) xx color(red)(3))
y + color(red)(2) = 1/3x - 1
y + color(red)(2) - 2 = 1/3x - 1 - 2
y + 0 = 1/3x - 3
y = color(red)(1/3)x - color(blue)(3)
