Question

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

x | y
5 | 7
6 | 18
7 | 29
8 | 40

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

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the first two points \((5, 7)\) and \((6, 18)\):
\( m=\frac{18 - 7}{6 - 5}=\frac{11}{1} = 11 \)

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \((5, 7)\) and \( m = 11 \):
\( y - 7=11(x - 5) \)
Expand the right - hand side: \( y - 7 = 11x-55 \)
Add 7 to both sides: \( y=11x - 55 + 7 \)
Simplify: \( y = 11x-48 \)
We can verify this equation with other points. For \( x = 7 \), \( y=11\times7-48=77 - 48 = 29 \) (which matches the table). For \( x = 8 \), \( y=11\times8-48=88 - 48 = 40 \) (which also matches the table).

Answer:

\( y = 11x-48 \)