Question

question 1-23
which of the following linear functions has the same slope as the slope of the line shown in this graph?
graph of a line on a coordinate plane
options:

1. a table with x values -2, -1, 0, 1, 2 and y values -14, -6, 2, 10, 18
2. a table with x values -2, -1, 0, 1, 2 and y values 11, 7, 3, -1, -5
3. -4x + y = 13
4. y = 2x + 8

Explanation:

Step1: Find slope of given graph

From the graph, two points on the line: (0, 7) and (2, -1) (approx, or (0, 7) and (1, 3) as per grid). Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 7}{1 - 0} = -4 \) (or using (0,7) and (2,-1): \( \frac{-1 - 7}{2 - 0} = -4 \)).

Step2: Check slope of each option

• First table: Slope between (0,2) and (1,10): \( \frac{10 - 2}{1 - 0} = 8 \).
• Second table: Slope between (0,3) and (1,-1): \( \frac{-1 - 3}{1 - 0} = -4 \).
• Third option (\(-4x + y = 13\)): Rewrite as \( y = 4x + 13 \), slope \( 4 \).
• Fourth option (\(y = 2x + 8\)): Slope \( 2 \).

Answer:

The second table (x: -2, -1, 0, 1, 2; y: 11, 7, 3, -1, -5) and the equation \(-4x + y = 13\) has slope -4? Wait, no, second table slope is -4. Wait, first table slope 8, second table slope -4, third equation slope 4, fourth slope 2. The graph has negative slope, steep. So the second table (x from -2 to 2, y:11,7,3,-1,-5) has slope -4, same as graph. Also, check the equation \(-4x + y = 13\) is \( y = 4x +13 \) (slope 4, positive). Wait, maybe I miscalculated graph slope. Let's recheck graph: when x=0, y=7; x=1, y=3 (since from (0,7) down 4, right 1: slope -4). Second table: x=0, y=3; x=1, y=-1: slope -4. Yes. So the second table (the one with y:11,7,3,-1,-5) and also check the equation? Wait, the options: first table (slope 8), second table (slope -4), third equation (slope 4), fourth (slope 2). So the correct option is the second table (the middle option with x -2,-1,0,1,2 and y 11,7,3,-1,-5) and also check the equation \(-4x + y = 13\) is slope 4, no. Wait, maybe the graph's slope is -4, so second table (slope -4) and let's check the equation \(-4x + y = 13\) is \( y = 4x +13 \) (slope 4, positive). So the second table (x: -2, -1, 0, 1, 2; y:11,7,3,-1,-5) has slope -4, same as graph. So the correct option is the second table (the one with y values 11,7,3,-1,-5) and also the equation? Wait, no, the options are: first table, second table, \(-4x + y =13\), \(y=2x+8\). So the second table (slope -4) matches the graph's slope (which is -4). So the answer is the second table (the option with x -2,-1,0,1,2 and y 11,7,3,-1,-5).