Write the equation of a line with a slope of 2/5 and passes through the point (2,3)

         y - 3 = ⁵/₂(x - 2)     {the point-slope form of the equation}

         y = ⁵/₂x - 2            {the slope-intercept form of the equation}

         5x - 2y = 4           {the standard form of the equation}

Step-by-step explanation:

The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.

m = ⁵/₂

(2, 3)    ⇒   x₀ = 2,  y₀ = 3

So, the point-slope form of the equation:

y - 3 = ⁵/₂(x - 2)

Therefore:

y - 3 =  ⁵/₂x - 5         {add 3 to both sides}

y = ⁵/₂x - 2              ←  the slope-intercept form of the equation

-⁵/₂x + y = - 2           {multiply both sides by (-2)}

5x - 2y = 4              ←  the standard form of the equation