SOLUTION: The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
If the relationship between cost
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Question 720148: The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
If the relationship between cost and the number of chairs produced is linear, how do I write an equation that expresses this relationship?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it costs 2200 to manufacture 100 chairs in a day.
it costs 4800 to manufacture 300 chairs in one day.
since there is a linear relationship, your relationship will be on a straight line.
you want to find the slope of this straight line and you want to find the y-intercept of this straight line.
to graph this relationship, you will want to show the number of chairs manufactured on the x-axis and the cost on the y-axis.
the slope of your line is equal to the formula:
slope = (y2 - y1) / (x2 - x1)
since it costs 2200 to manufacture 100 chairs, assign the value of 100 chairs to x1 and the value of 2200 dollars to y1.
since it costs 4800 to manufacture 300 chairs, assign the value of 300 chairs to x2 and the value of 4800 dollars to y2.
now you have the following values that you can use to solve for the slope.
you have:
x1 = 100
y1 = 2200
x2 = 300
y2 = 4800
you slope formuls of (y2 - y1) / (x2 - x1) becomes:
slope = (4800 - 2200) / (300 - 100)
this simplifies to:
slope = 2600 / 200 which simplifies further to 13 / 1 which is equal to 13.
you now have the slope of the equation of your line and all you need is the y-intercept.
this is the value of y when x is equal to 0.
to find the y-intercept, you can use the point slope form of the equation for a straight line.
the point slope form is:
y = y1 = m * (x - x1)
(x1,y1) can be any point on the line.
we'll assign the value of (100,2200) to the point (x1,y1).
this means that:
x1 = 100
y1 = 2200
m is equal to the slope which we have already figured out is equal to 13.
the point slope form of the equation becomes:
y - 2200 = 13 * (x - 100)
we solve this equation for y to get:
y = 13 * (x - 100) + 2200.
we simplify this equation to get:
y = 13x - 1300 + 2200.
we simplify this equation further to getr:
y = 13x + 900.
the equation i now in the slope intercept form of the equation for a straight line.
that form is y = m*x + b where m is the slope and b is the y-intercept.
consequently, the slope is equal to 13 and the y-intercept is equal to 900.
the y-intercept is the value of y when the value of x is equal to 0.
we can graph the equation of y = 13x + 900 as shown below:
your equation is:
y = 13x + 900
you can see from the graph that, when x = 100, y = 2200, and when x = 300, y = 4800.
this agrees with the problem statement, so the graph is accurate which means that the equation is accurate.
when x = 0, you can also see from the graph that the value of y is equal to 900.
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