Question

fill in the missing numbers to complete the linear equation that gives the rule for this table.
x | y
5 | 2
6 | 3
7 | 4
8 | 5
y = \square x - \square

Explanation:

Step1: Find the slope (m)

The slope \( m \) of a line 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 first two points \((5, 2)\) and \((6, 3)\). Then \( m=\frac{3 - 2}{6 - 5}=\frac{1}{1} = 1 \).

Step2: Find the y - intercept (b)

The equation of a line is \( y=mx + b \). We know \( m = 1 \), and we can use a point, say \((5, 2)\), to find \( b \). Substitute \( x = 5 \), \( y = 2 \), and \( m = 1 \) into the equation: \( 2=1\times5 + b \). Solving for \( b \), we get \( b=2 - 5=- 3 \). So the equation is \( y=x-3 \).

Answer:

The first box (coefficient of \( x \)) is \( 1 \) and the second box (constant term) is \( 3 \). So \( y=\boxed{1}x-\boxed{3} \)