Page 123 - Math Course 3 (Book 1)

Linear Equations: Rate of Change

Let’s Begin

Positive Slope Zero Slope

Example Example

Find the slope of the line that passes through Find the slope of the line that passes through
(–3, 2) and (5, 5). (–3, 4) and (4, 4).

Let (–3, 2) = (x , y ) and (5, 5) = (x , y ). Let (–3, 4) = (x , y ) and (4, 4) = (x , y ).
2
1
1
2
1
2
2
1
y – y rise y – y rise
2
2
m = x – x 1 run m = x – x 1 run
2 1 2 1
5 – 2 4 – 4
m = Substitute. m = Substitute.
5 – (–3) 4 – (–3)
3 0
= Simplify. = or 0 Simplify.
8 7
Answer The slope is 3 Answer The slope is 0
8
Negative Slope Undefined Slope

Example Example

Find the slope of the line that passes through Find the slope of the line that passes through
(–3, –4) and (–2, –8). (–2, –4) and (–2, 3).

Let (–3, 4) = (x , y ) and (–2, –8) = (x , y ).
1 1 2 2 Let (–2, –4) = (x , y ) and (–2, 3) = (x , y ).
1 1 2 2
y – y rise y – y rise
2
2
m = x – x 1 1 run m = x – x 1 1 run
2
2
–8–(–4) 3–(–4) 7
m = Substitute. m = or
–2–(–3) –2–(–2) 0
–4
= or –4 Simplify.
1

Since division by zero is
Answer The slope is –4 Answer undefined, the slope is undefined.

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