How Do You Write and Use a Prediction Equation?

We have a scatter plot of 6 points
The points (6,14) and (14,10) allow us to find the slope, -0.5
We can use a point and the slope to find the point-slope form of the line
Then we can convert it to slope-intercept form
Our equation gave us the point (16,9), which means that after 16 months there will be 9 staph infections

1. A 'line of fit' is a line that fits closely to the set of data on a scatter plot
1. We can use these two points with the slope formula to find the slope of the line
1. 'm' stands for slope
2. ∆y means the change in y-coordinates and ∆x means the change in x-coordinates
3. We've plugged (6,14) in for (x₁,y₁) and (14,10) in for (x₂,y₂)
1. Point slope form is y-y₁=m(x-x₁)
1. Point slope form is y-y₁=m(x-x₁)
2. We found 'm' in step 3 - so we can plug -0.5 in for 'm'
3. We labeled one of our points (x₁, y₁) in step 2, so we can plug 6 in for x₁ and 14 in for y₁
1. You'll have to distribute the -0.5 first
2. Then you'll have to add 14 to both sides
1. Distributing the -0.5, we get -0.5x-[(-0.5)•6]
2. -[(-0.5)•6]=+3
3. Then we can add 14 to both sides to solve for y
4. y=-0.5x+17 is the slope-intercept form of the line
1. Since we have a slope-intercept form of this line, we can estimate the number of staph infections by plugging 16 months into the equation
1. The number of months is represented by 'x', so we can plug 16 in for x to find the number of staph infections
2. -0.5•16=-8
3. -8+17=9
4. Our equation gave us the point (16,9), which means that after 16 months there will be 9 staph infections

Draw a line of fit for the data given and write its equation in slope-intercept form. Then use the equation to predict the number of staph infections at a hospital 16 months after the initial outbreak.