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Question 90579This question is from textbook
: Please help me with this equation.
Graph the following,
The line that has a slope of -2 and passes through the point(-3,5)
Thank You,
This question is from textbook
Found 2 solutions by Earlsdon, bucky:
Answer by Earlsdon(6294)   (Show Source):
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Since you are given the slope of the graph, it makes sense to use the slope-intercept
form of an equation. This form is:
.
y = mx + b
.
in which m is the slope. The problem tells you that the slope is -2, so in the slope-intercept
form you can substitute -2 for m and the equation then becomes:
.
y = -2x + b
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The problem also tells you that the point (-3, 5) is on the graph. This means that the
equation is satisfied when x equals -3 and y equals +5. So in the slope-intercept equation
that we are working on you can substitute -3 for x and +5 for y to get:
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+5 = (-2)(-3) + b
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Do the multiplication on the right side to get:
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+5 = +6 + b
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Solve for b by subtracting +6 from both sides and you have:
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-1 = b
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So now you know that the slope m is -2 and the value of b (which is the point on the y-axis
where the graph crosses that axis) is -1. Substitute those two values into the slope-intercept
form and the equation becomes:
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y = -2x - 1
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That is the equation you are trying to graph. Since you now know that the graph crosses the
y-axis at the point y = -1, you can put a dot on the graph at that point. Then you know
that the graph slopes at the rate -2 meaning that for every 1 unit you go horizontally
you move 2 units down. Put your pencil at the point -1 on the y-axis. Then move horizontally
1 unit ... stop there and then move down vertically 2 units and put a dot there. You should
be at the point (1, -3) and that point is on the graph. From that point you can again move
horizontally 1 unit and then down vertically 2 units. You should be at the point (2, -5) and
that point is on the graph. You can also plot the given point (-3, 5) as a point on the graph.
.
This gives you 4 points on the graph ... (-3, 5), (0, -1), (1, -3) and (2, -5). These points
can then be connected by running a straight line through them and that is the graph.
.
Another way you could locate points is to go to the equation we developed:
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y = -2x - 1
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and assign values that you choose for x and calculate the corresponding value of y. For example,
suppose you choose to let x = -1. Substitute that value into the equation and you get:
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y = (-2)(-1) - 1 = +2 - 1 = +1
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This tells you that when x = -1 then y = +1, so the point (-1, +1) is on the graph.
You can repeat this process for other values of x to get other points that can be connected
to give you the graph. When you get enough points to satisfy yourself that you know what
the graph looks like, you can run a straight line through the points to see the graph.
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The graph should look like:
.
.
Hope this helps you to understand the process that you can use to solve this problem.
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