Question

a table of values of a linear function is shown below.
x | -1 | 0 | 1 | 2 | 3
y | -9 | -5 | -1 | 3 | 7
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 using two points

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

Step3: Write linear equation

Use slope-intercept form $y=mx+b$, where $m=4$ (slope) and $b=-5$ (y-intercept).
$y=4x-5$

Answer:

y-intercept: $-5$
slope: $4$
equation: $y=4x-5$