3. Section 2.3 - 2. Linear Functions - Core Connections Integrated I, 2013

a Since we want to find the equation of a line, we have to determine its slope

m

and

y -

intercept

b .

When we have this information we can write the equation in slope-intercept form.

y = m x + b

We are told that the slope is

m = 1.5,

so we can substitute this into the slope-intercept form.

y = 1.5 x + b

To find

b,

let's substitute the given point in our equation and isolate

b .

y = 1.5 x + b

$x = 21$ , $y = 32$

32 = 1.5 (21) + b

32 = 31.5 + b

$LHS - 31.5 = RHS - 31.5$

0.5 = b

Rearrange equation

b = 0.5

Now, we can complete the equation.

y = 1.5 x + 0.5

b To find the coordinates of a third point on our line, we can substitute any value of

x

in the equation and find the corresponding

y -

value. Let's take

x = 2 .

y = 1.5 x + 0.5

$x = 2$

y = 1.5 (2) + 0.5

y = 3 + 0.5

Add terms

y = 3.5

Thus, a third point on the line is

(2, 3.5) .

Exercise 94 Page 98