Question

write the linear equation that gives the rule for this ta
x | y
4 | 53
5 | 68
6 | 83
7 | 98
write your answer as an equation with y first, followed

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 \((4, 53)\) and \((5, 68)\).
\( m=\frac{68 - 53}{5 - 4}=\frac{15}{1} = 15 \)

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((4, 53)\) and \( m = 15 \).
\( y-53 = 15(x - 4) \)

Step3: Simplify the equation

Expand the right - hand side: \( y-53=15x-60 \)
Add 53 to both sides: \( y=15x-60 + 53 \)
\( y=15x-7 \)
We can verify this equation with other points. For example, when \( x = 6 \), \( y=15\times6-7=90 - 7 = 83 \) (which matches the table), and when \( x = 7 \), \( y=15\times7-7=105 - 7 = 98 \) (which also matches the table).

Answer:

\( y = 15x-7 \)