Math Problem Statement

Complete the table of values for y = 2x + 3 and draw the graph on the grid.

Solution

The image contains a question regarding a linear function y=2x+3y = 2x + 3. Here's the breakdown of the solution:


Part (a): Completing the table of values

The equation y=2x+3y = 2x + 3 is given. To complete the table, substitute each value of xx into the equation to calculate yy:

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

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

  3. For x=0x = 0: y=2(0)+3=0+3=3y = 2(0) + 3 = 0 + 3 = 3

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

  5. For x=2x = 2: y=2(2)+3=4+3=7y = 2(2) + 3 = 4 + 3 = 7

  6. For x=3x = 3: y=2(3)+3=6+3=9y = 2(3) + 3 = 6 + 3 = 9

Thus, the completed table is:

\hline x & y \\ \hline -2 & -1 \\ -1 & 1 \\ 0 & 3 \\ 1 & 5 \\ 2 & 7 \\ 3 & 9 \\ \hline \end{array}$$ --- ### Part (b): Drawing the graph To plot the graph, mark the points $$(-2, -1)$$, $$(-1, 1)$$, $$(0, 3)$$, $$(1, 5)$$, $$(2, 7)$$, and $$(3, 9)$$ on the given grid. The red line in the image represents the graph of $$y = 2x + 3$$. --- ### Summary: - **The table is complete and correct.** - **The graph accurately represents the function $$y = 2x + 3$$.** Would you like further details or have any questions? --- Here are 5 related questions for practice: 1. How would the graph change if the equation was $$y = 2x - 1$$? 2. What is the slope of the line $$y = 2x + 3$$? 3. Can you find the $$x$$-intercept of the line $$y = 2x + 3$$? 4. What does the $$y$$-intercept represent on the graph? 5. How would you complete the table for $$y = -x + 2$$? **Tip**: Always remember that the slope $$m$$ in $$y = mx + c$$ determines the steepness of the line, and $$c$$ gives the $$y$$-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

y = mx + c (Slope-Intercept Form)

Theorems

Linear Relationship: A straight line is represented by y = mx + c.

Suitable Grade Level

Grades 6-8