Linear Equations
• Equations are like recipes!
• They tell us how to make a picture
(graph) of a function
•We just have to know how to read the
recipe…
Slope-Intercept Form (S-IF)
• y = mx + b
• b is the y-intercept.
▫ Tells us where to begin.
• m is the slope.
▫ Tells us how to move.
Graphing from S-IF
• Plot y-intercept first (on the Y-AXIS!!)
• Use the slope to plot more points.
▫ Remember: Slope is rise !
run
Example:
y = 2x – 4
Example:
• Graph
You Try!
• Graph y = -3x + 6
Writing Equations from Graphs
• In slope-intercept form:
• Find the y-intercept
▫ This is b!
• Count the slope and reduce
▫ This is m!
•Write equation
▫ Leave x and y, just replace m and b!
Example:
•Write an equation in S-IF for the graph
shown. (Draw in the points first!)
• y = ____ x + ____
Example:
•Write an equation in S-IF for the graph
shown.
You Try!
•Write an equation in S-IF for the graph
shown.
Point-Slope Form (P-SF)
• y = m(x – x1) + y1
•m is still slope
• x1 and y1 are coordinates of a point
(x1, y1) on the line
Graphing from P-SF
1. Write the ordered pair for your point
(x1, y1)
▫ Need to change the sign of the x-coordinate
since it’s y = m(x – x1) + y1
▫ For example, the point for y = 2(x + 3) – 1
is (-3, -1).
2. Plot that point.
3. From there, use the slope (m) to plot
more points
Example:
• Graph y = (x + 4) + 3
Example:
• Graph y = 4(x – 3) + 5
You Try!
• Graph y = -(x + 2) – 4
Writing Equations from Graphs
• In point-slope form:
• Find ANY point on the line
▫ This is (x1, y1)!
• Count the slope and reduce
▫ This is m!
•Write equation y = m(x – x1) + y1
▫ Leave x and y, just replace m, x1 and y1!
Example:
•Write an equation in P-SF for the graph
shown.
y = ___(x - ___) +___
Example:
•Write an equation in P-SF for the graph
shown.
You Try!
•Write an equation in P-SF for the graph
shown.
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