To complete the table of values for the equation $ y = 2x + 5 $, we will substitute each given $ x $-value into the equation and calculate the corresponding $ y $-value.
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Step 1: Understand the equation
The equation is $ y = 2x + 5 $.
This means:
→ Multiply the $ x $-value by 2.
→ Then add 5 to that result.
→ That gives you the $ y $-value.
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Step 2: Calculate for each x-value
Let’s go one by one:
1.
When $ x = -7 $:
$ y = 2(-7) + 5 = -14 + 5 = -9 $
2.
When $ x = -5 $:
$ y = 2(-5) + 5 = -10 + 5 = -5 $
3.
When $ x = -2 $:
$ y = 2(-2) + 5 = -4 + 5 = 1 $
4.
When $ x = 0 $:
$ y = 2(0) + 5 = 0 + 5 = 5 $
5.
When $ x = 2 $:
$ y = 2(2) + 5 = 4 + 5 = 9 $
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Step 3: Fill in the table
| x | -7 | -5 | -2 | 0 | 2 |
|-----|-----|-----|-----|-----|-----|
| y | -9 | -5 | 1 | 5 | 9 |
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Step 4: Plot the points on the graph
You are told to plot the points below each set of coordinates — meaning, for each $ x $-value in the table, plot the point $ (x, y) $ on the graph paper.
So the points to plot are:
- $ (-7, -9) $
- $ (-5, -5) $
- $ (-2, 1) $
- $ (0, 5) $
- $ (2, 9) $
After plotting these points, draw a straight line through them — since this is a linear equation, all points should lie on a straight line.
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Final Answer:
The completed table is:
| x | -7 | -5 | -2 | 0 | 2 |
|-----|-----|-----|-----|-----|-----|
| y | -9 | -5 | 1 | 5 | 9 |
Plot the points: (-7, -9), (-5, -5), (-2, 1), (0, 5), (2, 9) and draw a straight line through them.
Parent Tip: Review the logic above to help your child master the concept of linear graphing worksheet.
