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 . Here's the breakdown of the solution:
Part (a): Completing the table of values
The equation is given. To complete the table, substitute each value of into the equation to calculate :
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For :
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For :
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For :
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For :
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For :
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For :
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.Ask a new question for Free
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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