algebra i chapter 4: graphing linear equations and...
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Alg I Chapter 4 Notes.notebook
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Algebra I
Chapter 4:
Graphing Linear Equations and Functions
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4.2 Graph Linear EquaonsReminder:
Coordinate Plane is the area with the x and y axes that we use to graph
Ordered Pair describes a location on the coordinate plane (x, y)
3x + 4y = 12
3x + 4y = 12 makes a line when graphed.
Transformation a change in an image that is based on a rule applied to the coordinates
Translation a "slide" in which each point in an image moves the same distance in the same direction
Reflection a "flip"
Vertical Stretch each point is moved away from the x axis, while points on the axis remain fixed
Vertical Shrink each point is moved toward the x axis, while points on the axis remain fixed
Alg I Chapter 4 Notes.notebook
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Example 1: Standardized Test Pracce1. Substitute.2. Simplify.
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Example 2: Graph an Equaon1. Solve for y.2. Make a table of values. YOU get to choose the input values.
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Example 3: Graph y=b and x=a
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Example 4: Graph a Linear Funcon1. Make a table of values. YOU get to choose the input values. 2. Plot the points.3. Connect the points with a RAY!4. Identify the range.
Alg I Chapter 4 Notes.notebook
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Example 5: Solve a Mul‐Step Problem
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Example 6: Solve a Related Problem
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4.3 Graph Using Intercepts
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Example 1: Find the intercepts of the graph of an equaon
1. Substitute 0 for x to find the yintercept.2. Solve for y. Write it as an ordered pair.3. Substitute 0 for y to find the x intercept.4. Solve. Write it as an ordered pair.
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Example 2: Use Intercepts to Graph an Equaon1. Find the x and y intercepts. Write them as ordered pairs.2. Plot the points.3. Draw a lkine through the points.
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Example 3: Use a graph to Find Intercepts
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Example 4: Solve a Mul‐Step Problem
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Example 5: Use a Linear Model
The submersible starts at an elevation of –13,000 feet and ascends to an elevation of 0 feet.
So, the range of the function is –13,000 ≤ e ≤ 0.
The domain of the function is 0 ≤ t ≤ 20.
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4.4 Find Slope and Rate of Change
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Example 1: Find a Posive Slope
When given two points, use the slope formula to find slope.
Check:
Check:
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Example 2: Find a Negave Slope
When given two points, use the slope formula to find slope.
Check:
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Example 3: Find the Slope of a Horizontal Line
When given two points, use the slope formula to find slope.
Check:
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Example 4: Find the Slope of a Vercal Line
When given two points, use the slope formula to find slope.
Check:
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Example 5: Find a Rate of Change
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Example 6: Use a Graph to Find and Compare Rates of Change
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Example 7: Interpret a Graph
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4.5 Graph Using Slope‐Intercept Form
y = 3x + 4
Parallel lines have the EXACT SAME slopes!Line a has m = 3
Line b has m = 3
These lines are parallel!
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Example 1: Idenfy Slope and y‐intercept
The equation MUST be in slopeintercept (y=) form to easily identify the slope and yintercept.
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Example 2: Graph an Equaon Using Slope‐Intercept Form
1. Make sure the equation is in slopeintercept form! (y=)2. Identify the slope and yintercept.3. Plot the yintercept.4. Use the slope (rise over run) to plot another point.5. Draw a line through the points.
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Example 3: Change Slope of Lines
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Example 4: Change Intercepts of Lines
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Example 5: Idenfy Parallel LinesParallel lines have the EXACT SAME slopes!1. Find the slope of each line.
2. Compare the slopes.
3. If slopes are the same, the lines are parallel. If not, the lines are not parallel.
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4.6 Model Direct Variaon
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Example 1: Idenfy Direct Variaon Equaons
1. Make sure the equation is in slope intercept form. (y=)2. If the yintercept is 0, then it IS a direct variation equation.3. The constant of variation is the slope of the line.
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Example 2: Graph Direct Variaon Equaons
1. Make sure the equation is in slope intercept form. (y=)2. Graph like normal.
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Example 3: Write and Use a Direct Variaon Equaon
1. Write the direct variation equation.2. Substitute the x for the x in your ordered pair.3. Solve for a.
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Example 4: Solve a Mul‐Step Problem
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Example 5: Use a Direct Variaon Model