Question

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

x | y
3 | 7
4 | 8
5 | 9
6 | 10

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

submit

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say (3, 7) and (4, 8). Then $m = \frac{8 - 7}{4 - 3} = \frac{1}{1} = 1$.

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$. Plug in $m = 1$ and a point, like (3, 7). So $7 = 1\times3 + b$. Solving for b: $7 - 3 = b$, so $b = 4$.

Step3: Write the equation

Using $y = mx + b$ with $m = 1$ and $b = 4$, we get $y = x + 4$.

Answer:

$y = x + 4$