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Question 281373: Graph the line thru (1,1) wiht a slope of 3
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The slope of 3 means that for a change of 1 'x' there will be a change of 3 'y'.
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m = rise/run = 3/1
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We have the point (1,1), so the next point would be (2,4). With two points, you can graph a straight line.
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Or we can address the problem in terms of y = mx + b, which is the slope-intercept form of an equation.
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y = 3x + b
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But then the question is, "What is the value 'b' to be sure it goes through the point (1,1)?"
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Well, (1,1) means that when x=1, y =1, so we can show this as:
1 = 3(1) + b
b = -2
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This suggests the equation of the line with slope = 3 that goes through the point (1,1) is:
y = 3x -2
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Graphing it we can see...
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That looks correct.
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We also can do additional checking.
Some other points of interest are the y-intercept and the x-intercept.
The y-intercept is where x=0.
y = 3(0)-2 = -2
(0, -2)
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The x-intercept is where y=0.
0 = 3x -2
x = 2/3
(2/3, 0)
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By inspecting the graph, you can see these points are on the line, too.
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Done
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