Answer:
2. The y-intercept is 33 ft. The ball is 33 feet away from the wall.
3. It will take the ball 11 seconds to touch the wall.
4. The slope is -3 ft. The ball is rolling toward the wall at 3 ft per second
Step-by-step explanation:
Let x be the number of seconds.
We are told that a ball is rolling at a rate of 3 ft per second toward a wall that is 33 feet away.
Since the ball is rolling towards wall at a rate of 3 ft per second. This means that remaining distance between wall and ball is decreasing 3 ft with each passing second. Hence, the slope of our line will be negative 3 ft.
As initially ball was 33 feet away from wall, so our y-intercept will be 33.
Upon substituting our values in slope-intercept form of equation we will get equation of our line representing remaining distance between ball and wall after x seconds as:
[tex]y=-3x+33[/tex]
Let us find the number of seconds that ball will take to touch the wall by finding the x-intercept of our line. Since x-intercept is the point when line crosses x-axis and at this point y equals 0. The x-Intercept of a line is obtained by putting the value of y as zero in the equation of a line.
[tex]0=-3x+33[/tex]
[tex]0-33=-3x+33-33[/tex]
[tex]-33=-3x[/tex]
[tex]\frac{-33}{-3}=\frac{-3x}{-3}[/tex]
[tex]11=x[/tex]
Therefore, after 11 seconds ball will touch the wall.
Upon looking at our choices we can see that 2nd, 3rd and 4th options are correct choices.
