To graph the equation 6x + 7y = 18, rearrange the equation in the slope-intercept form (y = mx + b):
7y = -6x + 18
y = (-6/7)x + 18/7
Now we can identify the slope (m) and y-intercept (b) to get a clear picture of the line:
slope (m) = -6/7
y-intercept (b) = 18/7
The slope tells us that for every 7 units we move to the right along the x-axis, we move 6 units down along the y-axis. The y-intercept tells us that the line intersects the y-axis at the point (0, 18/7).
To graph this line, plot the y-intercept (0, 18/7) as a point on the graph. Then, using the slope, find another point by moving 7 units to the right and 6 units down from the y-intercept. Connect the two points with a straight line to complete the graph.
6x+7y=18
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