Question

question 4:
a scatterplot is shown.
scatterplot image
which statement about the scatterplot is true?
a. there is no association between x and y.
b. there is a positive, linear association between x and y.
c. there is a negative, linear association between x and y.
d. there is a nonlinear association between x and y
question 5:
an expression is shown.
$2.1 \times 10^5 + 4.3 \times 10^4$
which expressions is equivalent?
a. $2.53 \times 10^4$
b. $2.53 \times 10^5$
c. $6.4 \times 10^5$
d. $6.4 \times 10^9$
question 6:
create an equation for the line that passes through (2, 4) and (3, 6).

Explanation:

Question 4

Observe the scatterplot: as x increases, y consistently decreases in a roughly straight pattern, indicating a negative linear relationship.

Step1: Rewrite to same exponent

$2.1 \times 10^5 = 21 \times 10^4$

Step2: Add the coefficients

$21 \times 10^4 + 4.3 \times 10^4 = (21 + 4.3) \times 10^4 = 25.3 \times 10^4$

Step3: Convert to proper scientific notation

$25.3 \times 10^4 = 2.53 \times 10^5$

Step1: Calculate slope $m$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 4}{3 - 2} = 2$

Step2: Find y-intercept $b$

Use $(x,y)=(2,4)$: $4 = 2(2) + b \implies b=0$

Step3: Write line equation

$y = mx + b$

Answer:

C. There is a negative, linear association between x and y

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Question 5