Question 647903
When you are given the slope of a line and a point on that line and are asked to find the equation of the line itself, we use the 'point-slope' formula.

The point slope formula is as follows:

y - y1 = m( x - x1 )

You replace x1 with the 'x' coordinate from the point given, y1 with the 'y' coordinate from the point given, and 'm' with the slope given.

Step 1: Let's begin by substituting what we have into the point-slope formula

Point-slope formula: y - y1 = m( x - x1 )
Point given: (5,6)
Slope given: m = 2/3
{{{(y-6) = (2/3)(x-5)}}}

Step 2: Distribute the (2/3) to everything in the parenthesis

{{{(y-6) = (2/3)(x-5)}}}
{{{(y-6) = (2x/3)-10/3}}}

Step 3: Combine like terms by adding 6 to both sides to get 'y' by itself

{{{(y-6) = (2x/3)-10/3}}}
{{{(y) = (2x/3)-10/3 + 6/1}}}

Step 4: Find the LCD so you can add the fractions together. The least common denominator here is '3' because the least number that both fractions can go into is '3'

{{{(y) = (2x/3)-10/3 + 6/1}}}

Step 5: Multiply (6/1) to 3 on both the numerator and denominator to be able to add the fractions

{{{(y) = (2x/3)-10/3 + (6/1)(3/3)}}}
{{{(y) = (2x/3)-10/3 + 18/3}}}

Step 6: Add the fractions because they have the same denominators now

{{{(y) = (2x/3)-10/3 + 18/3}}}
{{{(y) = (2x/3)+8/3}}}

The equation of the line is {{{(y) = (2x/3)+8/3}}}