Math Problem Statement

Fill in the tables for the equations y = 3x, y = 2x, y = x + 3, y = x - 1, and y = -2x + 5.

Solution

It looks like you have an image of several tables with equations. I'll go ahead and solve each one, filling in the missing values for the tables.

1. y=3xy = 3x

xx001122
yy3(0)=03(0) = 03(1)=33(1) = 33(2)=63(2) = 6

Completed table:

xx012
yy036

2. y=2xy = 2x

xx00112233
yy2(0)=02(0) = 02(1)=22(1) = 22(2)=42(2) = 42(3)=62(3) = 6

Completed table:

xx0123
yy0246

3. y=x+3y = x + 3

xx−2-2−1-1001122
yy−2+3=1-2 + 3 = 1−1+3=2-1 + 3 = 20+3=30 + 3 = 31+3=41 + 3 = 42+3=52 + 3 = 5

Completed table:

xx-2-1012
yy12345

4. y=x−1y = x - 1

xx00112233
yy0−1=−10 - 1 = -11−1=01 - 1 = 02−1=12 - 1 = 13−1=23 - 1 = 2

Completed table:

xx0123
yy-1012

5. y=−2x+5y = -2x + 5

xx−2-2−1-1001122
yy−2(−2)+5=4+5=9-2(-2) + 5 = 4 + 5 = 9−2(−1)+5=2+5=7-2(-1) + 5 = 2 + 5 = 7−2(0)+5=0+5=5-2(0) + 5 = 0 + 5 = 5−2(1)+5=−2+5=3-2(1) + 5 = -2 + 5 = 3−2(2)+5=−4+5=1-2(2) + 5 = -4 + 5 = 1

Completed table:

xx-2-1012
yy97531

Would you like a detailed explanation for any of these calculations? Here are some additional questions for practice:

  1. What would the equation y=3x+2y = 3x + 2 look like if plotted for values of x=−1,0,1x = -1, 0, 1?
  2. How does the slope of a line affect the steepness of the graph?
  3. What happens to the line y=2xy = 2x if the equation changes to y=2x+4y = 2x + 4?
  4. Can you explain how to find the y-intercept from an equation like y=−2x+5y = -2x + 5?
  5. How would you create a table for the equation y=x2y = x^2?

Tip: Always check the slope in a linear equation—this will tell you how fast the line rises or falls as xx changes.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

y = 3x
y = 2x
y = x + 3
y = x - 1
y = -2x + 5

Theorems

-

Suitable Grade Level

Grade 6-8

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