Answer:
#9 (x, y) = (6, 32)
#10 The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32
Explanation:
The graph legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)
However the associated table will help us determine this
The linear equation for a line is expressed as
y = mx + c
where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)
Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line
Let's take the two x values as x1=0 and x2=1 and use the table
For Kites-R Fun
x1 = 0 ==> y1 = 8. This is also the y-intercept, b
We see that the red line corresponds to x = 0, y = 8
x2 = 1 ==> y2 = 12
y2 - y1 = rise = Δy =12 - 8 = 4
x2 - x1 = Δx = 1 - 0 =1
Slope m = 4/1 = 4
Equation of Kites-R Fun is 4x + 8
For Windy Kites
x1 = 0 ==> y1 = 20
y-intercept = 20 or b = 20
x2 = 1 ==> y2 = 22
Rise = Δy =22 - 20 = 2
Run = Δx = 1 - 0 = 1
Slope = m, b = 20
Equation of blue line is
y = 2x + 20
The two equations are:
y = 4x + 8
y = 2x + 20
Equating right sides:
4x + 8 = 2x + 20
Move 2x to the left side and 8 to the right side:
4x + 2x + 8 - 8 = 2x - 2x + 20 -8
2x = 12
x = 6
For x = 6 the costs are the same
Plugging x = 6into equation y = 4x + 8:
y = 4(6) + 8 = 24 + 8 = 32
So the solution set is
(6, 32)
Looking at the graph we see the two lines intersect at this point
(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)
On the second part
For Kites-R-US, each kite costs $4
The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.