Q:

The following table shows the distance from the bus stop as a function of time:Time (in minutes)x Distance (in meters)f(x)0 453 406 359 3012 25Find 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

Accepted Solution

A:
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".