Question

1. what is the

equation of
the graphed
inequality?

a ( y leq -x + 1 )
c ( y < x - 1 )
b ( y < -x + 1 )
d ( y leq x - 1 )

1. simon invests $850 in an account

that earns 2% annual simple
interest.

part a
what type of function models
simon’s investment?
a linear
b exponential
c quadratic
d absolute value

part b
what is the value of simon’s
investment after 5 years? $

1. which equation is a line

perpendicular to the line
( y = \frac{2}{3}x + 5 )?
a ( y = \frac{2}{3}x + 9 )
c ( y = \frac{3}{2}x - 12 )
b ( y = -\frac{2}{3}x - 6 )
d ( y = -\frac{3}{2}x + 7 )

1. over what interval is the function

( f(x) = |2x + 6| ) increasing?
a ( -infty < x < -3 )
b ( -3 < x < infty )
c ( -infty < x < 3 )
d ( 3 < x < infty )

Explanation:

Question 17

Step1: Analyze the line

The graphed line has a slope of -1 and y - intercept at 1, so the equation of the line is \( y=-x + 1 \).

Step2: Determine the inequality

The line is solid (so the inequality includes equality, \( \leq \) or \( \geq \)) and the shaded region is above the line? Wait, no, looking at the graph, the shaded region: let's check a point. For example, (0,0): plug into \( y=-x + 1 \), \( 0\leq - 0+1=1 \), which is true. Wait, the line is solid, so the inequality is \( y\leq -x + 1 \) (option A) or \( y\geq -x + 1 \)? Wait, no, let's re - check. The line is going from (0,1) to (1,0), slope - 1. The shaded area: if we take a point in the shaded region, say (-2,2), plug into \( y=-x + 1 \), \( 2=-(-2)+1=3 \)? No, wait, maybe I made a mistake. Wait, the graph: the line is from (0,1) to (2, - 1)? Wait, no, the x - intercept: when \( y = 0 \), \( 0=-x + 1\Rightarrow x = 1 \)? Wait, the graph shows x - intercept at 2? Wait, maybe my initial slope calculation is wrong. Let's recalculate the slope. From (0,1) to (2, - 1): slope \( m=\frac{-1 - 1}{2-0}=\frac{-2}{2}=-1 \). So the line is \( y=-x + 1 \). Now, the line is solid, so the inequality is either \( y\leq -x + 1 \) or \( y\geq -x + 1 \). Let's take a test point in the shaded region. Let's take (-2,2): \( 2\leq -(-2)+1=3 \), which is true. So the inequality is \( y\leq -x + 1 \) (option A) because the line is solid (so \( \leq \) or \( \geq \)) and the test point satisfies \( y\leq -x + 1 \).

Simple interest formula is \( I = Prt \), and the amount \( A=P + I=P(1+rt) \), where \( P \) is principal, \( r \) is rate, \( t \) is time. This is a linear function because it is of the form \( A(t)=P+Prt=Prt + P \), which is a linear function (degree 1 in \( t \)). Exponential functions are for compound interest (\( A = P(1 + r)^t \)), quadratic functions have degree 2, and absolute value functions have the form \( |x| \). So the function is linear.

Step1: Recall the simple interest formula

The formula for simple interest is \( I=Prt \), where \( P=\$850 \), \( r = 2\%=0.02 \), and \( t = 5 \) years.

Step2: Calculate the interest

\( I=850\times0.02\times5=850\times0.1 = 85 \)

Step3: Calculate the amount

The amount \( A=P + I=850+85=\$935 \)

Answer:

A. \( y\leq -x + 1 \)

Question 18 - Part A