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 $(5, - 1)$ & $(- 3, 4)$

m = \frac{4 - ( - 1 )}{- 3 - 5}

▼

Simplify

SubNeg

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

m = \frac{4 + 1}{- 3 - 5}

AddSubTerms

Add and subtract terms

m = \frac{5}{- 8}

MoveNegDenomToFrac

Put minus sign in front of fraction

m = - \frac{5}{8}

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{5}{8},

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

(5, - 1) .

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

SubstituteValues

Substitute values

y - (- 1) = - \frac{5}{8} (x - 5)

SubNeg

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

y + 1 = - \frac{5}{8} (x - 5)

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{5}{8}

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

(5, - 1) .

y = - \frac{5}{8} x + b

SubstituteII

$x = 5$ , $y = - 1$

- 1 = - \frac{5}{8} \cdot 5 + b

▼

Solve for

b

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

- 1 = - \frac{2 5}{8} + b

AddEqn

$LHS + \frac{2 5}{8} = RHS + \frac{2 5}{8}$

- 1 + \frac{2 5}{8} = b

OneToFrac

Rewrite $1$ as $\frac{8}{8}$

- \frac{8}{8} + \frac{2 5}{8} = b

AddFrac

Add fractions

\frac{1 7}{8} = b

RearrangeEqn

Rearrange equation

b = \frac{1 7}{8}

Now that we know the

y -

intercept lies at

(0, \frac{1 7}{8}),

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

y = - \frac{5}{8} x + \frac{1 7}{8}

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