Question

writing a system of equations from tables
complete the statements about the system of linear equations represented by the tables.
the equation representing the left table is
representing the right table is
y = -1.5x - 3
y = 1.5x - 6
y = x - 4.5
y = 3x - 1.5

left table:

x	y
0	-6
1	-4.5
2	-3
3	-1.5

right table:

x	y
0	6.1
1	2.1
2	-1.9
3	-5.9

Explanation:

Step1: Find left table's slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(0,-6)$ and $(1,-4.5)$:
$m=\frac{-4.5-(-6)}{1-0}=\frac{1.5}{1}=1.5$

Step2: Find left table's y-intercept

The y-intercept $b$ is $y$ when $x=0$, so $b=-6$. Equation: $y=1.5x-6$

Step3: Find right table's slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(0,6.1)$ and $(1,2.1)$:
$m=\frac{2.1-6.1}{1-0}=\frac{-4}{1}=-4$ (Wait, check with $(1,2.1)$ and $(2,-1.9)$: $m=\frac{-1.9-2.1}{2-1}=\frac{-4}{1}=-4$. Now check y-intercept: $b=6.1$, so equation $y=-4x+6.1$. But from given options, match the left table first, then check right table's matching option. Wait, recheck left table: $x=3$, $y=1.5*3-6=4.5-6=-1.5$, which matches. Now check given options for right table: test $y=-1.5x-3$: $x=0$, $y=-3≠6.1$; $y=1.5x-6$: $x=0$, $y=-6≠6.1$; $y=x-4.5$: $x=0$, $y=-4.5≠6.1$; $y=3x-15$: $x=0$, $y=-15≠6.1$. Wait, correct left table equation is $y=1.5x-6$, which is an option.

Answer:

The equation representing the left table is $\boldsymbol{y=1.5x-6}$
(Note: The given options do not include the correct equation for the right table, but the only matching equation for the left table from the provided list is $y=1.5x-6$)