An equation in slope-intercept form follows a specific format.

y = m x + b

For an equation in this form,

m

is the slope and

b

is the

y -

intercept. Let's use the given points to calculate

m .

We will start by substituting the points into the Slope Formula.

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

Substitute $(4, - 2)$ & $(8, - 6)$

m = \frac{- 6 - ( - 2 )}{8 - 4}

▼

Simplify right-hand side

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

m = \frac{- 6 + 2}{8 - 4}

Add and subtract terms

m = \frac{- 4}{4}

Calculate quotient

m = - 1

A slope of

- 1

means that for every

1

horizontal step in the positive direction, we take

1

vertical step in the negative direction. Now that we know the slope, we can write a partial version of the equation.

y = - 1 x + b

To complete the equation, we also need to determine the

y -

intercept,

b .

Since we know that the given points will satisfy the equation, we can substitute one of them into the equation and solve for

b .

Let's use

(4, - 2) .

y = - 1 x + b

$x = 4$ , $y = - 2$

- 2 = - 1 (4) + b

▼

Solve for

b

- 2 = - 4 + b

$LHS + 4 = RHS + 4$

2 = b

Rearrange equation

b = 2

A

y -

intercept of

2

means that the line crosses the

y -

axis at the point

(0, 2) .

We can now complete the equation.

y = - 1 x + 2 \Leftrightarrow y = - x + 2

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