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
$y = 1.5x - 6$
the equation representing the right table is
$y = -4x + 6.1$
$y = -3x + 4$
$y = 4x - 3.75$
$y = 6.1x - 4$

left table:

x	y
1	-4.5
2	-3
3	-1.5

right table:

x	y
1	2.1
2	-1.9
3	-5.9

Explanation:

Step1: Identify slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Calculate right table slope

Use $(0,6.1)$ and $(1,2.1)$:
$m = \frac{2.1 - 6.1}{1 - 0} = -4$

Step3: Find right table y-intercept

When $x=0$, $y=6.1$, so $b=6.1$

Step4: Form right table equation

$y = mx + b = -4x + 6.1$

Answer:

The equation representing the right table is $\boldsymbol{y = -4x + 6.1}$
The system of equations is:
$\boldsymbol{y = 1.5x - 6}$
$\boldsymbol{y = -4x + 6.1}$