Question

Write an equation from slope-intercept form (

𝑦
=
𝑚
𝑥
+
𝑏
y=mx+b ) from the table below. Click Here for Help Video.

𝑥
x
𝑦
y
0
0
3
3
−
2
−2
1
1
−
4
−4
−
1
−1
−
6
−6
−
3
−3





𝑦

=
y =

𝑥

+
x +

Answer 1

To write the equation in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) from the data provided in the table.

Let's first analyze the points given in the table:

- (0, 0)
- (3, 3)
- (-2, -2)
- (1, 1)
- (-4, -4)
- (-1, -1)
- (-6, -6)
- (-3, -3)

From observing these points, we can see a clear linear relationship. It appears that as \( x \) increases, \( y \) increases proportionally.

To calculate the slope \( m \) between two points, we can use the formula:

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

Let's take two points from the table: (0, 0) and (3, 3).

Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (3, 3) \).

So,

\[
m = \frac{3 - 0}{3 - 0} = \frac{3}{3} = 1
\]

Now, we also notice that when \( x = 0 \), \( y = 0 \) which indicates that the y-intercept \( b = 0 \) as well.

Thus, we have:

- Slope \( m = 1 \)
- Y-intercept \( b = 0 \)

Now we can write the equation in slope-intercept form:

\[
y = 1x + 0
\]

This simplifies to:

\[
y = x
\]

Therefore, the equation from slope-intercept form is:

\[
y = x
\]