Question

write the linear equation that gives the rule for th
x | y
1 | 22
2 | 44
3 | 66
4 | 88
write your answer as an equation with y first, fol

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 \((1, 22)\) and \((2, 44)\). Then \( m=\frac{44 - 22}{2 - 1}=\frac{22}{1} = 22 \).

Step2: Use point - slope form to find the equation

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \). We can use the point \((1, 22)\) and \( m = 22 \). Substituting these values into the point - slope form, we get \( y-22 = 22(x - 1) \).

Step3: Simplify the equation

Expand the right - hand side: \( y-22=22x-22 \). Then add 22 to both sides of the equation: \( y=22x-22 + 22 \), which simplifies to \( y = 22x \).

Answer:

\( y = 22x \)