Question

a table of values of a linear function is shown below.
x | -2 | -1 | 0 | 1 | 2
y | -15 | -11 | -7 | -3 | 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 $x=0$, $y=-7$.

Step2: Calculate slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(0,-7)$ and $(x_2,y_2)=(1,-3)$.
$m=\frac{-3 - (-7)}{1 - 0}=\frac{4}{1}=4$

Step3: Write linear equation

Use slope-intercept form $y=mx+b$, where $m=4$ (slope) and $b=-7$ (y-intercept).
$y=4x-7$

Answer:

y-intercept: $-7$
slope: $4$
equation: $y=4x-7$