Question

unit 3 - equations and graphs
for the x - y table, fill in the missing entries for each ordered pair. then write the rule for the table ((y = mx + b)).
in (x) (square) 2 -2 8 0 4 15
out (y) 23 (square) 8 -4 26 2 (square) (square)
rule ((y = mx + b)=square)

Explanation:

Step1: Find slope $m$

Use points $(2,8)$ and $(0,2)$:
$$m=\frac{8-2}{2-0}=\frac{6}{2}=3$$

Step2: Find y-intercept $b$

Use $x=0,y=2$ in $y=mx+b$:
$$2=3(0)+b \implies b=2$$

Step3: State the rule

Substitute $m=3,b=2$:
$$y=3x+2$$

Step4: Find missing x (y=23)

Solve $23=3x+2$:
$$3x=23-2=21 \implies x=\frac{21}{3}=7$$

Step5: Find y when x=4

Substitute $x=4$ into rule:
$$y=3(4)+2=12+2=14$$

Step6: Find y when x=15

Substitute $x=15$ into rule:
$$y=3(15)+2=45+2=47$$

Answer:

Missing x-value: 7, Missing y-values: 14, 47, Rule: $y=3x+2$