Exercise 48 Page 264

Practice makes perfect

a To find the slope of a line passing through two points

(x_{1}, y_{1})

and

(x_{2}, y_{2}),

we can substitute their coordinates in the Slope Formula and simplify.

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

Substitute $(2, - 11)$ & $(- 2, 1)$

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

▼

Simplify right-hand side

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

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

Add and subtract terms

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

Calculate quotient

m = - 3

The slope of the line passing through

(- 2, 1)

and

(2, - 11)

m = - 3 .

b Since this is a line, we can write it on slope-intercept form.

y = m x + b

In this form,

m

is the slope and

b

is the

y -

intercept. From Part A we already know that the slope of this line is

- 3 .

y = - 3 x + b

To find the

y -

intercept, we can substitute one of the given points into this equation and solve for

b .

Let's use point

(- 2, 1) .

y = - 3 x + b

$x = - 2$ , $y = 1$

1 = - 3 (- 2) + b

▼

Solve for

b

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

1 = 3 \cdot 2 + b

1 = 6 + b

$LHS - 6 = RHS - 6$

- 5 = b

Rearrange equation

b = - 5

When we also know the

y -

intercept, we have enough information to write the line's equation.

y = - 3 x - 5

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