Question

determine if $y = -2x + 1$ is a linear function. complete the table by substituting values for $x$ into the equation to solve for the corresponding value of $y$, then graph.

$x$	$-2$	$0$	$2$
$y$	$\quad$	$\quad$	$\quad$
$(x, y)$	$\quad$	$\quad$	$\quad$

is this relation a linear function? explain

Explanation:

Step1: Substitute \( x = -2 \) into \( y = -2x + 1 \)

\( y=-2\times(-2)+1 = 4 + 1 = 5 \)

Step2: Substitute \( x = 0 \) into \( y = -2x + 1 \)

\( y=-2\times0 + 1 = 0 + 1 = 1 \)

Step3: Substitute \( x = 2 \) into \( y = -2x + 1 \)

\( y=-2\times2 + 1 = -4 + 1 = -3 \)

Step4: Check if it's a linear function

A linear function has the form \( y = mx + b \) (where \( m \) and \( b \) are constants). The equation \( y=-2x + 1 \) is in this form with \( m=-2 \) and \( b = 1 \), so it is a linear function.

Answer:

For \( x=-2 \), \( y = 5 \), ordered pair \((-2,5)\); for \( x = 0 \), \( y = 1 \), ordered pair \((0,1)\); for \( x = 2 \), \( y=-3 \), ordered pair \((2,-3)\). The relation \( y=-2x + 1 \) is a linear function because it is in the form \( y=mx + b \) (linear function form) with \( m=-2 \) and \( b = 1 \).