Question

1. $m = \underline{\quad\quad\quad}$ $b = \underline{\quad\quad\quad}$

$equation = \underline{\quad\quad\quad}$

$x$

$y$

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0

-1.5

1

1.5

2

4.5

3

7.5

4

10.5

Explanation:

Step1: Identify slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(0,-1.5)$ and $(x_2,y_2)=(1,1.5)$:
$m=\frac{1.5-(-1.5)}{1-0}=\frac{3}{1}=3$

Step2: Find y-intercept $b$

$b$ is $y$ when $x=0$. From table, $x=0$ gives $y=-1.5$, so $b=-1.5$

Step3: Write linear equation

Use slope-intercept form $y=mx+b$:
$y=3x-1.5$

Answer:

$M=3$
$b=-1.5$
$\text{Equation}=y=3x-1.5$