Question

write the linear equation that gives the rule for this table.
x | y
6 | 12
7 | 14
23 | 46
47 | 94
write your answer as an equation with y first, followed by an equals sign.
submit

Explanation:

Step1: Find the slope (m)

Take two points, e.g., (6, 12) and (7, 14). The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. So, $m = \frac{14 - 12}{7 - 6} = \frac{2}{1} = 2$.

Step2: Check the y-intercept (b)

Use the point-slope form $y - y_1 = m(x - x_1)$ with (6, 12) and $m = 2$. So, $y - 12 = 2(x - 6)$. Simplify: $y - 12 = 2x - 12$. Add 12 to both sides: $y = 2x + 0$, so $b = 0$.

Step3: Form the equation

Since $m = 2$ and $b = 0$, the linear equation is $y = 2x$.

Answer:

$y = 2x$