pohaj49061
contestada

The following table shows the distance from the bus stop as a function of time:


Time (in minutes)
x Distance (in meters)
f(x)
0 45
3 40
6 35
9 30
12 25


Find and interpret the meaning of the x-intercept in this scenario.
(45, 0); the distance away from the bus stop
(27, 0); the time it takes to reach the bus stop
(45, 0); the time it takes to reach the bus stop
(27, 0); the distance away from the bus stop

Respuesta :

luisejr77

Answer: LAST OPTION.

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{40-45}{3-0}=-\frac{5}{3}[/tex]  

 By definition, the line intersects the y-axis when the value of "x" is zero ([tex]x=0[/tex]).

Based on the table, the y-intercept is:

[tex]b=45[/tex]

Then the equation of the line is:

[tex]y=-\frac{5}{3}x+45[/tex]

The line intersects the x-axis when the value of "y" is zero ([tex]y=0[/tex]), then you can substitute these value into the equation  and solve for "x":

[tex]0=-\frac{5}{3}x+45\\\\x=27[/tex]

So, you get the point:

[tex](27,0)[/tex]

Since the table shows the distance from the bus stop as a function of time, you can conclude that meaning of the x-intercept in this scenario is: "The distance away from the bus stop".

Answer: (27, 0); the distance away from the bus stop

Otras preguntas