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Linear Equations and Graphs

Linear Equations and Graphs. Vocabulary. Relation Input Output Function Domain Range. Scatter Plot Linear Equation x - intercept y - intercept Slope Rise Run.

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Linear Equations and Graphs

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  1. Linear Equations and Graphs

  2. Vocabulary • Relation • Input • Output • Function • Domain • Range • Scatter Plot • Linear Equation • x - intercept • y- intercept • Slope • Rise • Run

  3. Relation: a set of ordered pairs that relates an input to an output.Input: a number on which a function operates.Output: a number produced by evaluating a function using a given input.Function: a pairing of each number in a given set with exactly one number in another set.Domain: the set of all possible input values for the function.Range: the set of all possible output values for a function.

  4. Scatter plot: The graph of a set of data pairs (x,y), which is a collection of points in a coordinate plane.Slope: is the ratio of the rise (vertical change) to the run (horizontal change) between any two points on the line.Rise: the vertical change between two points on a line.Run: the horizontal change between two points on a line.x - intercept: the x coordinate of the point where the graph intersects the x-axis.y - intercept: the y coordinate of the point where the graph intersects the y-axis.

  5. Vocabulary Input Output Function Rule y = 1/2x + 2 Domain 2, 4, 6, 8, 10 Range 3, 4, 5, 6, 7

  6. Writing a Function Rule Step 1: Use the form y= mx+ b in which m is the slope and b is the y- intercept Step 2: Find the value of m. m= change in output change in input

  7. Writing a Function Rule Step 3: Substitute the value of m into the form y= mx+ b Step 4: Substitute an input – output pair for x and y to find the value of b or • Use the m to find the value of • y when x = o Step 5: Substitute the value of b into the form y= mx+ b

  8. Writing a Function Rule Example: Step 3: Substitute for m y= 3x + b • Step 4: • Use an input output pair to substitute for x and y • (1,4) • 4 = 3 (1) + b • 4 = 3 + b • 4 – 3 = 3 -3 + b • 1 = b • Step 5: • Substitute for b y= 3x + 1 Step 1: Use the form y= mx+ b Step 2: Find the value of m. m= (7-4) = 3 = 3 (2-1) 1

  9. Making an input – output table for a Function Rule Step 1: Choose several values to substitute for x. Step 2: • Substitute for x into the function rule. Step 3: • Solve for y to find the output for each input. Step 4: • Write the input and output as a pair in the table.

  10. Making an input – output table for a Function Rule Example: y = 4x - 2 Step 1: x = 1 , 2, 3, 4 Step 2: y = 4 (1) - 2 Step 3:y = 4 (1) – 2 y = 4 – 2 y = 2 when x = 1

  11. Graphing a Linear Equation Step 1: Choose several values to substitute for x. Step 2: • List the solution in a table as ordered pairs. Step 3: • Plot the ordered pairs. Step 4: • Draw a line through them.

  12. Graphing a Linear Equation Example: y = 3x - 3. (3,6) (2,3) Step 1: • x = 0, 1, 2, 3 (1,0) (0,-3) • Step 2: Step 3: • Plot the ordered pairs. Step 4: • Draw a line through them.

  13. Interpreting Scatter Plots Step 1: Plot the order pairs from the table. Step 2: • Label the horizontal and vertical axes. Step 3: • Identify the relationship that exists between two sets of data.

  14. Interpreting Scatter Plots Positive Relationship: The y – coordinates increases as the x – coordinates increases. Negative Relationship: The y – coordinates decreases as the x – coordinates increases. No Relationship: No obvious pattern exists between thecoordinates.

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