Question

Write an equation from slope-intercept form (

𝑦
=
𝑚
𝑥
+
𝑏
y=mx+b ) from the table below.

𝑥
x
𝑦
y
0
0
2
2
5
5
−
3
−3
10
10
−
8
−8
15
15
−
13
−13





𝑦

=
y =

𝑥

+
x +

Answer 1

To find the equation in slope-intercept form \( y = mx + b \) from the given table, we start by identifying the slope \( m \) and the y-intercept \( b \).

First, let's observe the values of \( x \) and \( y \) from the table:

\[
\begin{aligned}
(0, 0) \\
(2, 2) \\
(5, 5) \\
(-3, -3) \\
(10, 10) \\
(-8, -8) \\
(15, 15) \\
(-13, -13)
\end{aligned}
\]

From these observations, we can deduce that the relationship between \( x \) and \( y \) seems to always result in \( y = x \). Now, we can calculate the slope \( m \) using two points, for instance, \( (0, 0) \) and \( (2, 2) \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]

Next, since the point \( (0, 0) \) is on the line, it tells us that the y-intercept \( b \) is \( 0 \).

Thus, the equation in slope-intercept form is:

\[
y = 1x + 0
\]

This simplifies to:

\[
y = x
\]

Therefore, putting it in the format requested, the final equation is:

\[
y = x + 0
\]