Question

fill in the missing numbers to complete the linear table.

x	y
0	-55
1	-34
2	-13
3	8

( y = square x - square )

Explanation:

Step1: Find the slope (m)

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the points \((0, -55)\) and \((1, -34)\). Then \( m=\frac{-34 - (-55)}{1 - 0}=\frac{-34 + 55}{1}=21 \).

Step2: Find the y-intercept (b)

The equation of a line is \( y = mx + b \). When \( x = 0 \), \( y = b \). From the table, when \( x = 0 \), \( y=-55 \), so \( b=-55 \). But the equation is given as \( y=\square x-\square \), so we can rewrite \( y = 21x-55 \) (since \( y=21x+(- 55)=21x - 55 \)).

Answer:

The first box (coefficient of \( x \)) is \( 21 \) and the second box (the constant term) is \( 55 \). So the equation is \( y = 21x-55 \), so the missing numbers are \( 21 \) and \( 55 \).