Linear Equations and Graphs Vocabulary Relation Input Output

Linear Equations and Graphs

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

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.

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.

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

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

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

Writing a Function Rule Example: Step 3: x y 1 4 2 7 3 10 4 13 Step 1: Use the form y= mx + b Step 2: Find the value of m. m= (7 -4) = 3 (2 -1) 1 Substitute for m y= 3 x + 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= 3 x + 1

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.

Making an input – output table for a Function Rule Example: y = 4 x - 2 Step 1: x y 1 2 2 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 3 4

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.

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

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.

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 the coordinates.