To graph the equation 2x + 3y = 6 using the slope and y-intercept, we need to rearrange the equation in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation 2x + 3y = 6, we move the 2x term to the other side:
3y = -2x + 6
Next, we divide both sides by 3 to isolate the y term:
y = (-2/3)x + 2
Now, we can identify the slope and y-intercept:
The coefficient of x, -2/3, is the slope of the line.
The constant term, 2, is the y-intercept.
Using this information, we can plot the y-intercept at (0, 2) on the graph and then use the slope to find additional points.
The slope -2/3 means that for every 3 units we move to the right along the x-axis, we move down 2 units along the y-axis.
Using this information, we can plot additional points:
Starting from (0, 2), we can move 3 units to the right and 2 units down to get the point (3, 0).
Plotting these points and drawing a line through them, we get the graph of 2x + 3y = 6:
Graph of 2x + 3y = 6
Graph 2x + 3y = 6 using the slope and y-intercept.
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