Question

tell whether the given ordered pairs satisfy

1. {(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)}

2.

x	6	3	0	-3
y	6	3	0	-3

1. lily plans to volunteer at the tutoring center for 45 hours. she can tutor 3 hours per week. the function f(x) = 45 - 3x gives the number of hours she will have left to tutor after x weeks. graph the function and find its intercepts. what does each intercept represent?

described by 2x - 3y = 6.

Explanation:

Step1: Analyze the function

The function is \( f(x) = 45 - 3x \), which is a linear function in the form \( y = mx + b \) (here \( y = f(x) \), \( m=-3 \), \( b = 45 \)). To graph it, we can find the intercepts.

Step2: Find the x - intercept

The x - intercept is the value of \( x \) when \( y = 0 \) (or \( f(x)=0 \)).
Set \( f(x)=0 \):

$$
LATEXBLOCK0
$$

So the x - intercept is \( (15,0) \). This represents the number of weeks after which Lily will have 0 hours left to volunteer (she has completed all 45 hours of volunteering).

Step3: Find the y - intercept

The y - intercept is the value of \( y \) (or \( f(x) \)) when \( x = 0 \).
Substitute \( x = 0 \) into \( f(x)=45 - 3x \):
\( f(0)=45-3\times0 = 45 \)
So the y - intercept is \( (0,45) \). This represents the initial number of hours Lily plans to volunteer (before she starts tutoring, i.e., at week 0).

Step4: Graph the function

We can plot the two intercepts \( (0,45) \) and \( (15,0) \) and draw a straight line through them since it is a linear function. The slope of the line is \( - 3 \), which means that for each week that passes, the number of hours left to volunteer decreases by 3.

Answer:

• x - intercept: \( (15,0) \) (represents the number of weeks when Lily has 0 hours left to volunteer).
• y - intercept: \( (0,45) \) (represents the initial number of hours Lily plans to volunteer).
• Graph: A straight line passing through \( (0,45) \) and \( (15,0) \) with a slope of - 3.