First, we can obtain an equation for the line using the point-slope formula. 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 values from the problem gives:
(y - color(red)(5)) = color(blue)(5/3)(x - color(red)(3))
The standard form of a linear equation is:
color(red)(A)x + color(blue)(B)y = color(green)(C)
where, if at all possible, color(red)(A), color(blue)(B), and color(green)(C)are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
We can begin solving for this form by multiplying each side of the equation by color(purple)(3) to eliminate the fraction:
color(purple)(3)(y - color(red)(5)) = color(purple)(3) xx color(blue)(5/3)(x - color(red)(3))
3y - 15 = cancel(color(purple)(3)) xx color(blue)(5/cancel(3))(x - color(red)(3))
3y - 15 = 5x - 15
Next we can add color(red)(15) and subtract color(blue)(5x) to each side of the equation to isolate the constant on the right side of the equation while maintaining the balance of the equation.
-color(blue)(5x) + 3y - 15 + color(red)(15) = -color(blue)(5x) + 5x - 15 + color(red)(15)
-5x + 3y - 0 = 0 - 0
-5x + 3y = 0
Now, we can multiple each side of the equation by color(red)(-1) to make the coefficient of x positive or non-negative.
color(red)(-1)(-5x + 3y) = color(red)(-1) xx 0
5x - 3y = 0
