Question

1. a construction manager is monitoring the progress of the build of a new house. the scatterplot and table show the number of months since the start of the build and the percentage of the house still left to build. a linear function can be used to model this relationship.

new house
the table has two columns: number of months since start of build, x and percentage of house left to build, y. the rows are: 0, 100; 1, 86; 2, 65; 3, 59; 4, 41; 5, 34.
the scatterplot has x-axis as number of months since start of build (from 0 to 9) and y-axis as percentage of house left to build (from 0 to 100).
the multiple - choice options for the linear function are:
y = 7.3x - 97.8
y = - 13.5x + 7.3
y = - 13.5x + 97.8
y = 97.8x - 13.5

Explanation:

Step1: Identify slope and y-intercept

The linear equation is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the table, when \( x = 0 \), \( y = 100 \), so the y-intercept \( b \approx 97.8 \) (since the data is approximate). The slope \( m \) is negative (as \( y \) decreases with \( x \)). Calculate slope using two points, e.g., \( (0, 100) \) and \( (1, 86) \): \( m=\frac{86 - 100}{1 - 0}=-14 \), close to -13.5.

Step2: Match the equation

The equation with \( b\approx97.8 \) and negative slope \( m\approx - 13.5 \) is \( y=-13.5x + 97.8 \).

Answer:

\( y=-13.5x + 97.8 \) (the third option)