The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))
Where color(blue)(m) is the slope and color(red)(((x_1, y_1))) is a point the line passes through.
Substituting the slope and values from the points in the problem gives:
(y - color(red)(3)) = color(blue)(4/3)(x - color(red)(3))
We can solve for y to transform the equation to the slope-intercept form.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)(3) = (color(blue)(4/3) * x) - (color(blue)(4/3) * color(red)(3))
y - color(red)(3) = 4/3x - 4
y - color(red)(3) + 3 = 4/3x - 4 + 3
y - 0 = 4/3x - 1
y = color(red)(4/3)x - color(blue)(1)
