Answer: Option a.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Find the slope of the line with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose two points from the table and substitute the coordinates into the formula. Then, the slope is:
[tex]m=\frac{32-64}{4-0}=-8[/tex]
By definition, the line intersects the y-axis when the value of "x" is zero. So, based on the table, the y-intercept is:
[tex]b=64[/tex]
Then the equation of the line is:
[tex]y=-8x+64[/tex]
The line intersects the x-axis when the value of "y" is zero, then substituting y=0 into the equation of this line, and solving for "x", you get:
[tex]0=-8x+64\\\\-64=-8x\\\\x=8[/tex]
So, the point of intersection with the x-axis is:
[tex](8,0)[/tex]
Since the table shows the amount of air leaking from an inflatable as a function of time, you can conclude that meaning of the x-intercept in this scenario is: "The time it takes all the air to leave the inflatable".
Answer:
(8, 0); the time it takes all the air to leave the inflatable
Step-by-step explanation:
