Questions: ALCEBRA 1 REVIEW Name: K Date: 1-1 1. Which linear equation best represents the data plotted on the graph below? A. 2x+3y=-12 B. 3x+2y=-8 C. 2x-3y=12 D. 3x-2y=8

ALCEBRA 1 REVIEW
Name: K
Date:
1-1
1. Which linear equation best represents the data plotted on the graph below?
A. 2x+3y=-12
B. 3x+2y=-8
C. 2x-3y=12
D. 3x-2y=8

Transcript text: ALCEBRA 1 REVIEW Name: K K Date: $1-1$ 1. Which linear equation best represents the data plotted on the graph below? A. $2 x+3 y=-12$ B. $3 x+2 y=-8$ C. $2 x-3 y=12$ D. $3 x-2 y=8$

Solution

Solution Steps

Step 1: Find two points from the graph

Two points that are clearly on the gridlines of the graph are (2, -2) and (4, 0).

Step 2: Test the options with the two points

Substitute the x and y values of the points into each equation.

A. $2(2) + 3(-2) = 4 - 6 = -2 \neq -12$. This is not the correct equation.

B. $3(2) + 2(-2) = 6 - 4 = 2 \neq -8$. This is not the correct equation.

C. $2(2) - 3(-2) = 4 + 6 = 10 \neq 12$. This isn't correct, but let's check the second point to be sure. $2(4) - 3(0) = 8 - 0 = 8 \neq 12$. This is not the correct equation.

D. $3(2) - 2(-2) = 6 + 4 = 10 \neq 8$. This might be correct, so let's check the second point. $3(4) - 2(0) = 12 - 0 = 12 \neq 8$. Also incorrect.

Let's re-examine option C with another point from the graph. Try (6,2): $2(6) - 3(2) = 12 - 6 = 6 \neq 12$.

Step 3: Re-evaluate the points

It seems none of the given options work. Let's determine the equation of the line using the chosen points (2, -2) and (4, 0). Slope = $(0 - (-2))/(4-2) = 2/2 = 1$. Using point-slope form: $y - 0 = 1(x - 4) \Rightarrow y = x - 4$. Convert to standard form: $-x + y = -4$, or $x - y = 4$. Let's test another point from the graph such as (6,2): $6-2=4$, which is true.