Question

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

x	0	1	2	3	4
y	5	4	3	2	1

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

y-intercept:

slope:

equation:

Explanation:

Step1: Identify y-intercept

The y-intercept is the y-value when $x=0$. From the table, when $x=0$, $y=5$.

Step2: Calculate slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(1,4)$.
$m=\frac{4-5}{1-0}=\frac{-1}{1}=-1$

Step3: Write linear equation

Use slope-intercept form $y=mx+b$, where $m=-1$ (slope) and $b=5$ (y-intercept).
$y = -1x + 5$ or $y=-x+5$

Answer:

y-intercept: $5$
slope: $-1$
equation: $y=-x+5$