Question

1. which function could represent the values shown in the table?

x	1	2	3	4	5
y	1	4	7	10	13

a. $y = 2x - 1$ c. $y = 4x - 3$
b. $y = 3x - 2$ d. $y = 2x + 3$
for questions 8 - 11, find the slope of the line. give all answers in simplest form.
8.
graph of a line on a coordinate plane
$m = $
9.
graph of a line on a coordinate plane
$m = $
10.
graph of a line on a coordinate plane
$m = $
11.
graph of a line on a coordinate plane
$m = $

Explanation:

Question 7 (Function from Table)

Step1: Test Option A ($y = 2x - 1$)

For $x = 1$: $y = 2(1) - 1 = 1$ (matches). For $x = 2$: $y = 2(2) - 1 = 3$ (does not match table's $y = 4$). So A is wrong.

Step2: Test Option B ($y = 3x - 2$)

For $x = 1$: $y = 3(1) - 2 = 1$ (matches). For $x = 2$: $y = 3(2) - 2 = 4$ (matches). For $x = 3$: $y = 3(3) - 2 = 7$ (matches). For $x = 4$: $y = 3(4) - 2 = 10$ (matches). For $x = 5$: $y = 3(5) - 2 = 13$ (matches). So B works.

Step3: Test Option C ($y = 4x - 3$)

For $x = 1$: $y = 4(1) - 3 = 1$ (matches). For $x = 2$: $y = 4(2) - 3 = 5$ (does not match table's $y = 4$). So C is wrong.

Step4: Test Option D ($y = 2x + 3$)

For $x = 1$: $y = 2(1) + 3 = 5$ (does not match table's $y = 1$). So D is wrong.

Step1: Identify Two Points

From the graph, let's take two points: $(-2, 0)$ and $(2, -2)$ (approximate, based on grid).

Step2: Calculate Slope ($m = \frac{y_2 - y_1}{x_2 - x_1}$)

$m = \frac{-2 - 0}{2 - (-2)} = \frac{-2}{4} = -\frac{1}{2}$

Step1: Analyze the Line

The line is horizontal (parallel to x - axis). For a horizontal line, the slope is 0 (since $y$ - values don't change, $y_2 - y_1 = 0$).

Answer:

B. $y = 3x - 2$

Question 8 (Slope from Graph)