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 $(- 1, - 5)$ & $(2, 10)$

m = \frac{1 0 - ( - 5 )}{2 - ( - 1 )}

▼

Simplify right-hand side

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

m = \frac{1 0 + 5}{2 + 1}

Add terms

m = \frac{1 5}{3}

Calculate quotient

m = 5

A slope of

5

means that for every

1

horizontal step in the positive direction, we take

5

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

y = 5 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

(2, 10) .

y = 5 x + b

$x = 2$ , $y = 10$

10 = 5 (2) + b

▼

Solve for

b

10 = 10 + b

$LHS - 10 = RHS - 10$

0 = b

Rearrange equation

b = 0

A

y -

intercept of

0

means that the line crosses the

y -

axis at the point

(0, 0) .

We can now complete the equation.

y = 5 x + 0 \Leftrightarrow y = 5 x

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