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 $(- 8.3, - 5.2)$ & $(6.4, 9.5)$

m = \frac{9 . 5 - ( - 5 . 2 )}{6 . 4 - ( - 8 . 3 )}

▼

Simplify right-hand side

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

m = \frac{9 . 5 + 5 . 2}{6 . 4 + 8 . 3}

Add terms

m = \frac{1 4 . 7}{1 4 . 7}

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

y = 1 x + b \Leftrightarrow y = 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

(6.4, 9.5) .

y = x + b

$x = 6.4$ , $y = 9.5$

9.5 = 6.4 + b

▼

Solve for

b

$LHS - 6.4 = RHS - 6.4$

9.5 - 6.4 = 6.4 + b - 6.4

Subtract term

3.1 = b

Rearrange equation

b = 3.1

A

y -

intercept of

3.1

means that the line crosses the

y -

axis at the point

(0, 3.1) .

We can now complete the equation.

y = 1 x + 3.1 \Leftrightarrow y = x + 3.1

Exercise