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Notes #10Graph Equations of LinesGraph Equations of Lines

(Section 2‐3)

Family of functions: a group of functions with shared characteristics.

Parent function: The most basic function in a family of functions

y‐intercept: The y coordinate of a point where the graph intersects the y – axis

x‐intercept: The coordinate of a point where a graph intersects the x – axis

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Slope‐Intercept Form

y= mx + b 

with slope m and y ‐ intercept b

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. Compare the graph with the graph of y = x.

yExample 1

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. Compare the graph with the graph of y = x.

yExample 2

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. Compare the graph with the graph of y = x.

yExample 3

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. Compare the graph with the graph of y = x.

yExample 4

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. 

yExample 5

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. 

yExample 6 4x + 3y = 9

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph the equation. 

yExample 7 5x – 2y = 8

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Standard Form

Ax + By= C

where A and B are not both zero.

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Write each equation in standard form.

Example 8 2 3 7Example 8    2x = 3y + 7

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Write each equation in standard form.

Example 9 6 2 1Example 9    6y = ‐2x + 1

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Write each equation in standard form.

Example 10Example 10   

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

To find an x‐intercept set y= 0.

To find an y‐intercept set x= 0To find an y‐intercept set x= 0.

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Find the x and y‐intercepts of the given equation.

E l 11 2 2 0Example 11    2x + y  2 = 0

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Find the x and y‐intercepts of the given equation.

E l 12 6 4 5Example 12    6x + 4y=‐5

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

STANDARD FORM Graph the equation. Label any intercepts.

Example 13py

x

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

STANDARD FORM Graph the equation. Label any intercepts.

Example 14py

x

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Horizontal Lines are y= . Their slope is 0.

Vertical Lines are x= Their slope is undefinedVertical Lines are x=. Their slope is undefined.

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?

Graph.

E l 15 2y

Example 15   x=2

x

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Graph.

E l 16 3y

Example 16 y = ‐3

x

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Graph.

yExample 17 y = 5

x

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Graph.

E l 18 1y

Example 18 x = ‐1

x

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HW #14 pg 93 (1‐41 odd)

Standard: Prepare for 2.0Essential Question: How do you graph a linear equation? Essential Question...How do you graph a linear equation?