Question

solving a system represented in a table
the tables represent two linear functions. the equation represented by the first table is given below.
y = 5.75x + 34.5
what linear equation is represented by the second table?
dropdown
what is the solution to the system of equations?
options:
y = -2.5x - 15
y = -2.5x
y = 2.5x + 15
y = 2.5x

Explanation:

Step1: Find slope (m)

Choose two points from the second table, e.g., $(-4, -5)$ and $(-3, -7.5)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-7.5 - (-5)}{-3 - (-4)}=\frac{-2.5}{1}=-2.5$

Step2: Find y-intercept (b)

Use slope-intercept form $y=mx+b$, substitute $m=-2.5$ and point $(-4, -5)$:
$-5 = -2.5(-4) + b$
$-5 = 10 + b$
$b = -5 - 10 = -15$

Step3: Write linear equation

Substitute $m=-2.5$ and $b=-15$ into $y=mx+b$.
$y=-2.5x-15$

Answer:

$y = -2.5x - 15$