SOLUTION: Find an equation of the line that satisfies the given conditions. Through (5, 6); slope :2/3

Question 647903: Find an equation of the line that satisfies the given conditions.
Through (5, 6); slope :2/3

Answer by Algebraic(50) (Show Source): You can put this solution on YOUR website!
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

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

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

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'

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

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

The equation of the line is

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