Question

fill in the missing numbers to complete the linear equation that gives the rule for this table.
x | y
5 | 28
6 | 34
7 | 40
8 | 46
y = \square x - \square
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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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the first two points \( (5, 28) \) and \( (6, 34) \):
\( m=\frac{34 - 28}{6 - 5}=\frac{6}{1}=6 \)

Step2: Find the y - intercept (b)

The linear equation is \( y = mx + b \). We know \( m = 6 \) and can use the point \( (5, 28) \) to find \( b \). Substitute \( x = 5 \), \( y = 28 \), and \( m = 6 \) into the equation:
\( 28=6\times5 + b \)
\( 28 = 30 + b \)
Subtract 30 from both sides: \( b=28 - 30=- 2 \)

So the equation is \( y = 6x-2 \)

Answer:

\( y=\boxed{6}x-\boxed{2} \)