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To determine which graph matches the equation y+3=2(x+3), we first need to convert the equation to slope-intercept form (y = mx + c).
y + 3 = 2(x + 3) [Given equation]
Distribute the 2 on the right-hand side of the equation.
y + 3 = 2x + 6
Subtract 3 from both sides of the equation to isolate the y term.
y = 2x + 3
Now that we have the equation in slope-intercept form (y = mx + c), we can identify the slope and y-intercept. The slope of the line is 2 and the y-intercept is 3.
To graph the equation, we can start by plotting the y-intercept at point (0, 3). Then, using the slope of 2, we can find another point on the line by moving 1 unit to the right and 2 units up from the y-intercept. We can continue this process to plot additional points and draw a straight line through them.
Note that the line passes through the point (0, 3) and has a slope of 2.
To match the graph to the given equation, we can compare the features of the graph (such as its slope and y-intercept) to the features of the equation. The graph of y = 2x + 3 matches the equation y+3=2(x+3).
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