Question

a table of values of a linear function is shown below.

x	-2	-1	0	1	2
y	4	3	2	1	0

find the y-intercept and slope of the functions graph, and find the equation for the function.
y-intercept:
slope:
equation:

Explanation:

Step1: Find y-intercept

The y-intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 2 \). So the y-intercept is 2.

Step2: Calculate slope

The slope \( m \) of a linear function is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points, e.g., \( (0, 2) \) and \( (1, 1) \). Then \( m=\frac{1 - 2}{1 - 0}=\frac{-1}{1}=-1 \).

Step3: Find the equation

The slope - intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know \( m=-1 \) and \( b = 2 \), so the equation is \( y=-x + 2 \).

Answer:

y - intercept: \( 2 \)
slope: \( - 1 \)
equation: \( y=-x + 2 \)