Question

fill in the missing numbers to complete the linear equation table.

x	y
1	1
2	-11
3	-23

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 \( (0, 13) \) and \( (1, 1) \). Then \( m=\frac{1 - 13}{1 - 0}=\frac{- 12}{1}=- 12 \). We can check with another pair, say \( (1, 1) \) and \( (2, - 11) \). \( m=\frac{-11 - 1}{2 - 1}=\frac{-12}{1}=-12 \). So the slope \( m=-12 \).

Step2: Find the y - intercept (b)

The equation of a line in slope - intercept form is \( y = mx + b \), where \( b \) is the y - intercept. When \( x = 0 \), \( y=b \). From the table, when \( x = 0 \), \( y = 13 \). So \( b = 13 \).

Answer:

The equation of the line is \( y=-12x + 13 \). So the first box (coefficient of \( x \)) is \(-12\) and the second box (constant term) is \(13\).