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Question 110619: Write the equation of the line with given slope and y-intercept.
Then graph each line using the slope and y-intercept.
Slope: -2; y-intercept: (0, 4)
Thanks
JMS
Found 2 solutions by KATERIYA, bucky:
Answer by KATERIYA(1)   (Show Source):
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! You can do this problem without an equation if you would like. All you need is an understanding
of the concept of slope. The slope of a line can be interpreted as "If you go one unit horizontally
to the right from a point on the line, from that new point ... how many units do you go vertically
up or down to get back to the line.
.
In this problem you are told that one point on the line (the y-intercept) is (0, 4). That
point is on the y-axis at +4. Then you are told that the slope is -2. The minus sign tells
you that the slope is down as you go to the right. So you can start at the intercept
on the y-axis (because you know (0, 4) is on the graph. From that point go one unit
horizontally to the right and from there go down 2 units. Stop there and mark that point
because it is on the graph. Then starting from the new point you marked, you can again move
one unit horizontally to the right and from there go down 2 units and mark that as another
point on the graph. And once you get the hang of this process, you can do it in multiples.
For example, in this problem you could start at the y-intercept, and from there move 5 units
horizontally (this would put you at the point (5, 4) ) and then move down 10 units
(from 5 times the slope which is 5*-2). You should be at the point (5, -6) where the -6
comes from 4 - 10.
.
When you get done, your graph should look like this:
.
.
Hope this method doesn't confuse you too much. It may help you to understand the concept of
slope and how it relates to graphing.
.
If this method is not clear, you could always use the slope intercept form of an equation
to calculate other points on the graph. The slope intercept form is:
.
y = mx + b
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where m is the slope and b is the value of y where the graph crosses the y axis. In this
problem you were given that the slope (m) is -2 and that the graph crosses the y axis at +4.
Substituting these values into the equation converts it to:
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y = -2x + 4
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You can now use this equation to find other points on the graph. For example, previously
we found that the point (5, -6) is on the graph. So if we assume that x is 5 and plug that
value into the equation we get:
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y = -2*5 + 4 = -10 + 4 = -6
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This tells us that when x = 5 then y = -6 so the point (5, -6) is on the graph.
.
You can find other points on the graph by letting x be other values of your choice and
using the equation to compute the value of y that corresponds to each value of x. Then
plot the points you get.
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