Question

find the equation of the linear function represented by the table below in slope-intercept form.

x	y
-4	-1
1	4
6	9
11	14

answer attempt 1 out of 2

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's use the points $(-4, -1)$ and $(1, 4)$.
So, $m = \frac{4 - (-1)}{1 - (-4)} = \frac{5}{5} = 1$.

Step2: Find the y-intercept (b)

Using the slope-intercept form $y = mx + b$, we can substitute one of the points and the slope. Let's use the point $(1, 4)$ and $m = 1$.
Substitute into the equation: $4 = 1(1) + b$.
Simplify: $4 = 1 + b$.
Subtract 1 from both sides: $b = 4 - 1 = 3$.

Step3: Write the equation

Now that we have $m = 1$ and $b = 3$, the slope-intercept form is $y = x + 3$.

Answer:

$y = x + 3$