Question

from unit 2, lesson 10

1. a. consider the equation ( y = 1.5x + 2 ). find four pairs of ( x ) and ( y ) values that make the equation true. plot the points ( (x,y) ) on the coordinate plane.

b. based on the graph, can this be a proportional relationship? why or why not?
learning targets
+ i can describe the relationship between circumference and diameter of any circle.
+ i can explain what ( pi ) means.

Explanation:

Step1: Substitute \(x = 0\)

Substitute \(x = 0\) into \(y=1.5x + 2\).

$$y=1.5\times0 + 2=2$$

So, the pair is \((0,2)\).

Step2: Substitute \(x = 2\)

Substitute \(x = 2\) into \(y = 1.5x+2\).

$$y=1.5\times2+2=3 + 2=5$$

So, the pair is \((2,5)\).

Step3: Substitute \(x = 4\)

Substitute \(x = 4\) into \(y=1.5x + 2\).

$$y=1.5\times4+2=6 + 2=8$$

So, the pair is \((4,8)\).

Step4: Substitute \(x = 6\)

Substitute \(x = 6\) into \(y=1.5x + 2\).

$$y=1.5\times6+2=9+2 = 11$$

So, the pair is \((6,11)\).

For part b:
A proportional relationship has the form \(y=kx\) (where \(k\) is the constant of proportionality) and passes through the origin \((0,0)\).
The equation \(y = 1.5x+2\) has a \(y\) - intercept of \(2\) (when \(x = 0,y=2
eq0\)).

Answer:

a. Four pairs: \((0,2)\), \((2,5)\), \((4,8)\), \((6,11)\)
b. No. A proportional relationship \(y = kx\) passes through \((0,0)\), but \(y=1.5x + 2\) has \(y\) - intercept \(2\) (when \(x = 0,y=2\)).