In order to write both the slope-intercept form and the point-slope form, we need the slope of the line. To find the slope, we will use the given points and the Slope Formula.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePoints

Substitute $(0, - 2)$ & $(3, 2)$

m = \frac{2 - ( - 2 )}{3 - 0}

▼

Simplify

SubNeg

$a - (- b) = a + b$

m = \frac{2 + 2}{3 - 0}

AddSubTerms

Add and subtract terms

m = \frac{4}{3}

Now that we know the slope, let's form our equations. We will find them one at a time.

Point-Slope Form

Equations in point-slope form follow a specific format.

y - y_{1} = m (x - x_{1})

In this form,

m

is the slope of the line and

(x_{1}, y_{1})

is a point on the line. Since we know the slope of the line is

\frac{4}{3},

we can write the equation of the line in point-slope form. We can use either of the given points as

(x_{1}, y_{1})

in our equation. Let's use

(3, 2) .

y - 2 = \frac{4}{3} (x - 3)

Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!

Slope-Intercept Form

Equations in slope-intercept form also follow a specific format.

y = m x + b,

In this form,

m

represents the slope of the line and

b

represents the

y -

intercept. We already calculated the slope as

m = \frac{4}{3}

above. The next step is to substitute one of the points into the equation and solve for the

y -

intercept,

b .

Let's use the point

(0, - 2) .

y = \frac{4}{3} x + b

SubstituteII

$x = 0$ , $y = - 2$

- 2 = \frac{4}{3} \cdot 0 + b

ZeroPropMult

Zero Property of Multiplication

- 2 = b

RearrangeEqn

Rearrange equation

b = - 2

Now that we know the

y -

intercept lies at

(0, - 2),

we have what we need to write a slope-intercept form equation.

y = \frac{4}{3} x + (- 2) \Leftrightarrow y = \frac{4}{3} x - 2

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