Envision Math 2.0: Grade 8, Volume 1
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3. Use Linear Models to Make Predictions
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Exercise 4 Page 226

Practice makes perfect

The graph shows the relationship between the number of children and the amount of money spent on groceries.

We will predict the difference in the amount spent on groceries between a family with five children and a family with two children. We will use the slope to find the difference. The equation of the trend line is in slope-intercept form.

y= 21.08x+ 85.15 In this equation, 21.08 is the slope and 85.15 is the y-intercept of the line. Now remember that we can find the slope by dividing the vertical distance of two points by the horizontal distance of these two points. Slope=Vertical distance/Horizontal distance We are looking for the vertical distance, since we want to find the difference in the amount spent on groceries for a family with five children and a family with two children.

Now we will substitute the values into the Slope Formula.
Slope=Vertical distance/Horizontal distance
21.08=Vertical distance/3
Solve for Vertical distance
3* 21.08=Difference in vertical distance/3* 3
3* 21.08=Vertical distance
63.24=Vertical distance
Vertical distance=63.24
The vertical distance is 63.24. This means that the difference in the amount spent on groceries between a family with five children and a family with two children is about $ 63.24.
We will predict the number of children that a family has if the amount spent on groceries per week is about $169.47. We will find the x-value of the graph when the y- value is $169.47.

The estimated number of children in a family that spends $169.47 on groceries per week is 4.