Question

1. the y - intercept of the graph of 12x + 2y = 18 in the xy - plane is (0, y). what is the value of y? 14. a model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. this model is defined by an equation in the form f(x)=a + bx, where f(x) is the predicted weight, in pounds, of the animal x days after it was born, and a and b are constants. what is the value of a? 15. the graph shows the height above ground, in meters, of a ball x seconds after the ball was launched upward from a platform. which statement is the best interpretation of the marked point (1.0, 4.8) in this context? a) 1.0 second after being launched, the balls height above ground is 4.8 meters. b) 4.8 seconds after being launched, the balls height above ground is 1.0 meter. c) the ball was launched from an initial height of 1.0 meter with an initial velocity of 4.8 meters per second. d) the ball was launched from an initial height of 4.8 meters with an initial velocity of 1.0 meter per second.

Explanation:

13.

Step1: Find y - intercept

To find the y - intercept, set \(x = 0\) in the equation \(12x+2y = 18\).
When \(x = 0\), the equation becomes \(2y=18\).

Step2: Solve for y

Divide both sides of \(2y = 18\) by 2. We get \(y=\frac{18}{2}=9\).

Step1: Recall linear - function form

The linear function is \(f(x)=a + bx\), where \(a\) is the initial value and \(b\) is the rate of change.
The animal weighed 241 pounds when it was born (\(x = 0\)).

Step2: Determine the value of a

When \(x = 0\), \(f(0)=a + b\times0=a\). Since the weight at birth (\(x = 0\)) is 241 pounds, \(a = 241\).

In a coordinate - pair \((x,y)\) for a graph of height \(y\) versus time \(x\), the \(x\) - value represents time and the \(y\) - value represents height. For the point \((1.0,4.8)\), \(x = 1.0\) second and \(y = 4.8\) meters. It means 1.0 second after being launched, the ball's height above ground is 4.8 meters.

Answer:

9

14.