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 $(- 3, 4)$ & $(2, - 1)$

m = \frac{- 1 - 4}{2 - ( - 3 )}

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

m = \frac{- 1 - 4}{2 + 3}

Add and subtract terms

m = \frac{- 5}{5}

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 to solve for

b .

Let's use

(- 3, 4) .

y = - 1 x + b

$x = - 3$ , $y = 4$

4 = - 1 (- 3) + b

$- a (- b) = a \cdot b$

4 = 3 + b

$LHS - 3 = RHS - 3$

1 = b

Rearrange equation

b = 1

A

y -

intercept of

1

means that the line crosses the

y -

axis at the point

(0, 1) .

We can now complete the equation.

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

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