We can use the point-slope formula for writing the equation for the line in the problem. The point-slope form of a linear equation is: (y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))
Where (color(blue)(x_1), color(blue)(y_1)) is a point on the line and color(red)(m) is the slope.
Substituting the slope and values from the point in the problem gives:
(y - color(blue)(-3)) = color(red)(2/3)(x - color(blue)(2))
(y + color(blue)(3)) = color(red)(2/3)(x - color(blue)(2))
We can solve this equation for y to put the equation in slope-intercept format. 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(blue)(3) = (color(red)(2/3) xx x) - (color(red)(2/3) xx color(blue)(2))
y + color(blue)(3) = color(red)(2/3)x - 4/3
y + color(blue)(3) - 3 = color(red)(2/3)x - 4/3 - 3
y + 0 = color(red)(2/3)x - 4/3 - (3/3 xx 3)
y = color(red)(2/3)x - 4/3 - 9/3
y = color(red)(2/3)x - color(blue)(13/3)
