Question

write the linear equation that gives the rule for this table.

x	y
4	3
5	4
6	5

write your answer as an equation with y first, followed by an equals sign.

submit

Explanation:

Step1: Find the slope (m)

The slope \( m \) between 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 \((3, 2)\) and \((4, 3)\). Then \( m=\frac{3 - 2}{4 - 3}=\frac{1}{1} = 1 \).

Step2: Find the y - intercept (b)

The slope - intercept form of a linear equation is \( y=mx + b \). We know \( m = 1 \), and we can use one of the points, say \((3, 2)\). Substitute \( x = 3 \), \( y = 2 \) and \( m = 1 \) into the equation: \( 2=1\times3 + b \). Solve for \( b \): \( 2=3 + b \), so \( b=2 - 3=- 1 \).

Step3: Write the equation

Using the slope - intercept form \( y=mx + b \) with \( m = 1 \) and \( b=-1 \), we get \( y=x - 1 \).

Answer:

\( y = x - 1 \)