# Slope-Intercept and Point-Slope Forms of a Linear

To determine the equation of a line, you may use two
variations of the general form of a line.

These formulas are:

1)The Point-Slope Formula
(y – y_{1}) = m(x – x_{1})

2)The Slope-Intercept Formula y = mx + b

As the names imply the form that you use is dependant on the information you are given to start with.

**Example 1:** Find the equation of the line that has
a slope of 1/3 and contains the point (2, -1).

Solution

Since the information given is a point and the slope, the point slope formula is

used.

**Step 1: Substitute the given into the formula.**

Since m = 1/3 and P_{1} = (2, -1) then
x_{1} = 2 and y_{1} = -1.

(This the standard formula of the line)

**Step 2: Calculate P2.**

Select any value you with for x or y and substitute it
into the equation found in

step 1. For this example y will equal 2.

Therefore P_{2} = (11, 2)

**Step 3: Verify**.

When any two points of a line are substituted into the
slope formula the slope of

the line should be the answer. In this case, when
P_{1} and P_{2} are
substituted into

the slope formula the answer should be 1/3.

SinceP_{1} = (2, -1) and P_{2} = (11, 2) then x_{1} = 2, x_{2} = 11,
y_{1} = -1 and y_{2} = 2 then:

(The slopes are alike so the equation and
P_{2} are correct)

**Step 4: Graph**

The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

**Example 2:** Find the equation of the line that has
a slope of 2/3 and a y intercept of (0, 4).

Solution

### Step 1: Substitute the given into the formula.

Since the y intercept is (0, 4), b = 4 and the slope, m, is given as 2/3.

(Note: The standard form does not allow fractional values,
so you need to

resolve this by multiplying by the LCD of 3).

(This is the calculated equation of the line.)

### Step 2: Verify.

Plot 2 points using the formula. For this example
y_{1} = 2 and y_{2} = -6.

Therefore P_{1} = (-3, 2) and P_{2} = (-15, -6)

### Step 2:

Next the x and y values are substituted into the slope formula.

Since the slope found using the two points is also 2/3 the formula is correct