BCalculate the number of years between 1996 and 2020 and substitute their coordinates into the equation from Part A.
AExample Equation: y=525x+2100
BExample Answer: About 14 700 girls will participate in ice hockey in 2020.
Practice makes perfect
We are given a scatter plot and a graph of a line of best fit which shows the number of girls who participate in ice hockey.
We are asked to write an equation in slope-intercept form for the line that is drawn.
y=mx+bIn this equation, m is the slope and b is the y-intercept. To find the slope m, we will first identify the coordinates of two points that the line is passes through.
The line passes through the points with coordinates x_1= 5 and y_1 ≈ 4700. Also, the line passes through the point with coordinates x_2= 9 and y_2 ≈ 6700. Let's substitute these values into slope formula.
We found that the slope is equal to about m= 525. This means that the number of girls that participate in ice hockey is increasing by 525 every year.
y=mx+b
⇕
y= 525x+b
Next, let's find the y-intercept b, which is the y-value when x=0.
We can see that the y-intercept b is equal to about 2100. This means that in 1996, the number of girls participating in hockey was equal to about 2100. Finally, we will write an equation of our line of best fit in slope-intercept form.
y=525x+b ⇕
y=525+2100
Note that we were approximating the coordinates of the points, so your equation might be different.
In Part A, we wrote an equation which estimates the number of girls — represented with y — participating in ice hockey x years after the year 1996.
y=525x+2100We are asked to use this equation to make a conjecture about the number of girls participating in ice hockey in 2020. To do that, we first need to calculate the number of years x between 1996 and 2020.
x=2020-1996 ⇔ x=24
Now we can substitute x=24 into the equation from Part A to estimate the number of girls.
Using the equation, we estimated that about 14 700 girls will participate in ice hockey in 2020. Note that if your equation was different, your conjecture will also be different.
