Objective:
To graph linear equations using a table of values.Vocabulary:
- Coefficient - the number part of a term (the number directly in front of the variable)
- Plot - to graph on a coordinate plane. (Remember: To plot you Run and Jump.
- Straight Edge - Something with a straight edge, such as a ruler, protractor, identification card, etc.
Notes:
Construct a table with three columns labeled x, y, and whatever the equation is. You will be choosing numbers to put in the x column. Things to consider when picking these x values are:- If the equation has y by itself (ie. y = __x + __)...
- if the coefficient of x is a fraction then choose multiples of its denominator for your x values.
- Ex: The fraction is ¾ then use any of −8, −4, 0, 4, 8
- if the coefficient of x is not a fraction then choose any x you want. I like using −3, 0, and 3.
- if the coefficient of x is a fraction then choose multiples of its denominator for your x values.
- If the equation is in standard form (ie. Ax + By = C) ...
- If B ≠ 1 then use multiples of B for your x values.
- Ex: B = 5, then use any of −10, −5, 0, 5, 10
- If B is 1 then use any x value you want. I like using −3, 0, and 3.
- If B ≠ 1 then use multiples of B for your x values.
Examples:
1. Sketch the graph of y = −2x + 4.
Construct the table with three columns: x, y, and y = −2x + 4. Fill in the x column with the values your chosen (I chose −3, 0, and 3).
Find the corresponding y-values by substituting each x-value into the equation and solving.
Make sure to show each and every step. Write your answers in the y-column.Now that the table is complete plot the points for the solutions you found. For this example the points are (−3,−2), (0,4), and (3,10).
The points should create a straight line. If they don't you've made an error.
When they line up, use a straight-edge to draw the line through them.
Add arrows and label the line.
2. Sketch the graph of y = ½x −3.
Construct the table with three columns; x, y, and y = ½x −3 Fill in the x column with the values your chosen (I chose −4, 0, and 4 because they are multiples of the denominator of the coefficient of x (multiples of 2)).
Find the corresponding y-values by substituting each x-value into the equation and solving.
Make sure to show each and every step. Write your answers in the y-column.Now that the table is complete plot the points for the solutions you found. For this example the points are (−4, −5), (0,−3), and (4,−1).
The points should create a straight line. If they don't you've made an error.
When they line up, use a straight-edge to draw the line through them.
Add arrows and label the line.