Question

Gerald purchased 55 paving stones to use in his garden. The graph shows points representing the number of stones left to place at several different times while Gerald is working.

A function graph of a line segment having three points (0,55), (3,40) and (7, 20) with an x axis of zero to twelve Hours and a y axis of zero to sixty Paving Stones left



Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of paving stones left to place, y, and the time, x, Gerald has spent working.

Answer 1

Answer: 5x + y = 55

Step-by-step explanation:

Answer 2

The equation that represents the relationship between the number of paving stones left to place and the time is

`5x+y=55`

Solution-

In the graph, on the abscissa time in hours is represented and on the ordinate the number of stones left is represented.

From the graph we have three points, they are (0, 55), (3, 40), (7, 20)

Taking any two points and applying two point formula of straight line, we can get the equation or relation between the two variables.

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

Taking (0, 55), (3, 40)

`\Rightarrow (y-55)/(40-55)=(x-0)/(3-0)`

`\Rightarrow (y-55)/(-15)=(x)/(3)`

`\Rightarrow (y-55)/(-5)=x`

`\Rightarrow y-55=-5x`

`\Rightarrow 5x+y-55=0`

`\Rightarrow 5x+y=55`

Therefore, 5x+y=55 is the correct relationship that represents the number of paving stones left to play y and the time x Gerald has spent working.