Question

gerald purchased 55 paving stones to use in his garden. the graph shows points representing the number of stones left to place at different times while gerald is working. what equation in slope-intercept form would represent the relationship between the number of paving stones left to place, y, and the time, x, gerald has spent working? what do the slope and y-intercept mean in this situation? select from the drop-down menus to correctly complete the statements. the equation is y = choose... x + choose... the number of stones left to place is choose... at

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((0,55)\) and \((3,40)\), we have \( m=\frac{40 - 55}{3 - 0}=\frac{-15}{3}=-5 \).

Step2: Determine the y - intercept

The slope - intercept form of a line is \( y=mx + b \), where \( b \) is the y - intercept. The line passes through the point \((0,55)\). When \( x = 0 \), \( y=b \). So, \( b = 55 \).

Step3: Write the equation

Substituting \( m=-5 \) and \( b = 55 \) into the slope - intercept form \( y=mx + b \), we get \( y=-5x + 55 \).

Meaning of slope and y - intercept:

• The slope \( m=-5 \) means that Gerald places 5 paving stones per hour (since the number of stones left, \( y \), decreases by 5 for each increase of 1 in \( x \) (time in hours)).
• The y - intercept \( b = 55 \) means that when Gerald has spent 0 hours working (\( x = 0 \)), he has 55 paving stones left to place (which is the initial number of paving stones he had to place).

Answer:

\( y = -5x + 55 \)