Answer
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Step 1:: Recognize that the given equation is in the slope-intercept form, which is y = mx + b.
The given equation is $$y + 3 = 2(x + 3)$$.
To identify the graph that matches the given equation, first, rewrite the equation in the slope-intercepoint form.
Step 2:: Distribute the 2 on the right side of the equation:
y + 3 = 2x + 6
Step 3:: Subtract 3 from both sides to isolate y:
y = 2x + 6 - 3
Step 4:: Simplify the right side:
y = 2x + 3
Now the equation is in the slope-intercept form, where m = 2 and b = 3. The graph of the equation should have a slope of 2 and a y-intercept of 3.
Step 5:: Compare the equation with the given options and find the matching graph.
Option A: The slope is 1, and the y-intercept is 1, which does not match the calculated slope and y-intercept. Option B: The slope is - 1, and the y-intercept is - 1, which does not match the calculated slope and y-intercept. Option C: The slope is 2, and the y-intercept is 3, which matches the calculated slope and y-intercept. Option D: The slope is - 2, and the y-intercept is - 3, which does not match the calculated slope and y-intercept.
Step 6:: Identify the correct graph based on the comparison.
The correct graph is Option C.
Final Answer
The graph that matches the equation y + 3 = 2(x + 3) is Option C.
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