Step One
Write the point, slope form of the equation.
Givens
m (slope ) = 3
point = (2,5)
Equation
The general form for the equation is
(y - y1) = m(x - x1)
y1 = 5
x1 = 2
(y - 5) = 3(x - 2) <<<<< Answer point Slope.
Step Two
Solve Step 1 for the y intercept, slope form of the equation. All you do is remove the brackets of both sides of the equation.
y - 5 = 3x - 2*3
y - 5 = 3x - 6 Add 5 to both sides.
y = 3x - 6 + 5
y = 3x - 1
Note: You must write the formula so that y has no number in front of it and the number with no letter is on the same side as the term containing x. So -1 is on the same side of the equal sign as 3x.
Check
There are a couple of ways you could check this. One of the ways is to develop the y intercept and the slope form directly.
What you have so far.
y = 3x + b where b is the y intercept. Use the point to solve for b.
Givens
y = 5
x = 2
5 = 3(2) + b
5 = 6 + b Subtract 6 from both sides.
5 - 6 = b
b = - 1
y = 3x - 1
And it checks.
