Math Problem Statement

Complete the table of values for the equation 2y - 2 = 4x and plot the graph on the grid.

Solution

Part (a): Completing the Table of Values

The equation given is:

2y−2=4x2y - 2 = 4x

Rearrange it to solve for yy:

2y=4x+2  ⟹  y=2x+12y = 4x + 2 \implies y = 2x + 1

Substitute the xx-values into y=2x+1y = 2x + 1:

  1. For x=−1x = -1: y=2(−1)+1=−2+1=−1y = 2(-1) + 1 = -2 + 1 = -1

  2. For x=0x = 0: y=2(0)+1=0+1=1y = 2(0) + 1 = 0 + 1 = 1

  3. For x=2x = 2: y=2(2)+1=4+1=5y = 2(2) + 1 = 4 + 1 = 5

The completed table is:

\hline x & y \\ \hline -1 & -1 \\ 0 & 1 \\ 2 & 5 \\ \hline \end{array}$$ --- ### Part (b): Plotting the Graph Now, using the table of values, plot the points $$(-1, -1)$$, $$(0, 1)$$, and $$(2, 5)$$ on the grid. Connect them with a straight line, as the equation represents a linear relationship. --- Do you want a detailed explanation of the graph, or assistance plotting it? ### Related Questions: 1. How can you determine the slope of a line using its equation? 2. What is the y-intercept of the equation $$2y - 2 = 4x$$? 3. How can you verify if a point lies on a given line? 4. What is the geometric meaning of $$y = 2x + 1$$? 5. How would the graph change if the equation were $$2y - 2 = 6x$$? ### Tip: When plotting graphs, always double-check the points using the equation to ensure they align

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Math Problem Analysis

Mathematical Concepts

Linear equations
Graphing
Coordinate Geometry

Formulas

y = mx + c (equation of a straight line)

Theorems

Point-slope form of a line

Suitable Grade Level

Grades 6-8

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