Writing Linear Equations in Slope-Intercept Form

a

Let's start by recalling the slope-intercept form of a line.

y = m x + b

Here,

m

is the slope and

b

is the

y -

intercept. We will use the two given points to calculate these values. Let's find the slope

m

by substituting the points into the slope formula.

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

SubstitutePointsSubstitute

(0, 2)

&

(2, - 3)

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

SubTermsSubtract terms

m = \frac{- 5}{2}

CalcQuotCalculate quotient

m = - 2.5

Now that we know that the slope is

- 2.5,

we can write a partial equation of the line.

y = - 2.5 x + b

To complete the equation, we need to determine the

y -

intercept

b .

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

b .

Let's use

(0, 2) .

y = - 2.5 x + b

SubstituteII

x = 0

,

y = 2

2 = - 2.5 \cdot 0 + b

Solve for

b

MultiplyMultiply

2 = 0 + b

AddTermsAdd terms

2 = b

RearrangeEqnRearrange equation

b = 2

We know that the value of the

y -

intercept is

4 .

We can now complete the equation.

y = - 2.5 x + 2

b

The first step is to find the slope using the slope formula and the given points.

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

SubstitutePointsSubstitute

(- 4, - 3)

&

(1, - 2)

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

SubNeg

a - (- b) = a + b

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

AddTermsAdd terms

m = \frac{1}{5}

We have found that

m = \frac{1}{5} .

Let's substitute it into the slope-intercept form.

y = \frac{1}{5} x + b

To complete the equation, we also need to determine the

y -

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

b .

Let's use

(1, - 2) .

y = \frac{1}{5} x + b

SubstituteII

x = 1

,

y = - 2

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

Solve for

b

MultByOne

a \cdot 1 = a

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

SubEqn

LHS - \frac{1}{5} = RHS - \frac{1}{5}

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

NumberToFrac

a = \frac{5 \cdot a}{5}

\frac{5 ( - 2 )}{5} - \frac{1}{5} = b

MultiplyMultiply

\frac{- 1 0}{5} - \frac{1}{5} = b

SubFracSubtract fractions

\frac{- 1 0 - 1}{5} = b

SubTermSubtract term

\frac{- 1 1}{5} = b

MoveNegNumToFracPut minus sign in front of fraction

- \frac{1 1}{5} = b

RearrangeEqnRearrange equation

b = \frac{- 1 1}{5}

We have found that

b = - \frac{1 1}{5} .

We can now complete the equation.

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

Writing Linear Equations in Slope-Intercept Form 1.3 - Solution