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

and

b .

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

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

Substitute $(- 3, 4)$ & $(1, 12)$

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

▼

Simplify right-hand side

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

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

Add and subtract terms

m = \frac{8}{4}

Calculate quotient

m = 2

A slope of

2

means that for every

1

horizontal step in the positive direction, we take

2

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

y = 2 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

(1, 12) .

y = 2 x + b

$x = 1$ , $y = 12$

12 = 2 (1) + b

▼

Solve for

b

$a \cdot 1 = a$

12 = 2 + b

$LHS - 2 = RHS - 2$

10 = b

Rearrange equation

b = 10

A

y -

intercept of

10

means that the line crosses the

y -

axis at the point

(0, 10) .

We can now complete the equation.

y = 2 x + 10

Exercise 8 Page 246

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