Question

Write a linear equation in the form of y = mx + b for the following table.



𝑥
x
𝑦
y
0
0
4
4
4
4
−
3
−3
8
8
−
10
−10



𝑦
=
y=


𝑥
x
+
+

Answer 1

To write a linear equation in the form \( y = mx + b \) based on the given table, we first need to identify the slope \( m \) and the y-intercept \( b \).

From the table data, we have the following points:

1. \((0, 0)\)
2. \((4, 4)\)
3. \((4, -3)\)
4. \((8, 8)\)
5. \((-10, -10)\)

It appears that not all points provided are valid, especially since \((4, 4)\) and \((4, -3)\) share the same x-coordinate but have different y-values, which does not conform to a linear relationship. To facilitate finding a linear equation, we can consider the points that adhere to a linear relationship.

Let's take points \((0, 0)\) and \((8, 8)\), as they give a clearer view of a trend.

1. Determine the slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{8 - 0} = \frac{8}{8} = 1
\]

2. Determine the y-intercept \( b \):
From the point \((0, 0)\), when \( x = 0 \), \( y = 0 \). Thus, \( b = 0 \).

Putting this together, the equation becomes:
\[
y = 1x + 0 \quad \text{or simply} \quad y = x
\]

So, the linear equation based on the valid points that we can gather is:
\[
y = x
\]