Question

find the equation of the linear function in slope intercept form, y=mx + b
x y
2 -4
4 0
6 4
8 8
x y
1 -2
2 -1
3 0
4 1
x y
-3 -6
-1 2
1 10
3 18
x y
0 10
5 20
10 30
15 40

Explanation:

Step1: Calculate slope $m$

$m=\frac{y_2 - y_1}{x_2 - x_1}$. For first table, using $(2,-4)$ and $(4,0)$, $m=\frac{0 - (-4)}{4 - 2}=2$.

Step2: Find $y$-intercept $b$

Substitute $m = 2$ and $(x,y)=(2,-4)$ into $y=mx + b$. $-4=2\times2 + b$, so $b=-8$. Equation is $y = 2x-8$.

Step3: Repeat for second table

Using $(1,-2)$ and $(2,-1)$, $m=\frac{-1-(-2)}{2 - 1}=1$. Substitute $m = 1$ and $(x,y)=(1,-2)$ into $y=mx + b$. $-2=1\times1 + b$, $b=-3$. Equation is $y=x - 3$.

Step4: Third table

Using $(-3,-6)$ and $(-1,2)$, $m=\frac{2-(-6)}{-1-(-3)} = 4$. Substitute $m = 4$ and $(x,y)=(-3,-6)$ into $y=mx + b$. $-6=4\times(-3)+b$, $b = 6$. Equation is $y = 4x+6$.

Step5: Fourth table

Using $(0,10)$ and $(5,20)$, $m=\frac{20 - 10}{5-0}=2$. Since $x = 0,y = 10$, $b = 10$. Equation is $y=2x + 10$.

Answer:

First table: $y = 2x-8$
Second table: $y=x - 3$
Third table: $y = 4x+6$
Fourth table: $y=2x + 10$