Question

find the equation of the linear function represented by the table below in slope-intercept form.
$x$: 0, 1, 2, 3, 4
$y$: 5, 12, 19, 26, 33

Explanation:

Step1: Identify y-intercept (b)

When $x=0$, $y=5$, so $b=5$.

Step2: Calculate slope (m)

Use two points, e.g., $(0,5)$ and $(1,12)$.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{12-5}{1-0}=7$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=7$ and $b=5$.
$y=7x+5$

Answer:

$y=7x+5$