The problem gives the info. p=40 and x=52balloons. p=20 and x=62 balloons. I have to write and equation of the line for the demand using p=mx+b. I know I have to find the slope in order to do this.But have no idea how to do that with this info. Any suggestions. I think it starts 40=mx?+52 Help/
you have two data sets.
20=62m+b
40=52m+b
subtract equation 2 from 1
-20=10m
now you have m.
to solve for b, put that m into either equation, and solve for b.
To find the equation of a line using the point-slope form (p = mx + b), you need to determine the slope (m) and the y-intercept (b). In this case, the given information provides you with two points: (40, 52) and (20, 62).
To find the slope (m), you can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first set of points (40, 52) and (20, 62) to calculate the slope.
m = (62 - 52) / (20 - 40)
Simplifying this equation:
m = 10 / -20
m = -1/2
Now that we have the slope (m), we can substitute it into the point-slope form of the equation using one of the given points. Let's use the first set of points (40, 52).
p = m x + b
40 = (-1/2) * 52 + b
Simplify this equation:
40 = -26 + b
To isolate the term with b, add 26 to both sides of the equation:
40 + 26 = b
b = 66
Finally, substitute the values of m and b into the equation:
p = (-1/2) x + 66
Therefore, the equation for the demand using p = mx + b is p = (-1/2) x + 66.