Question

x-y
0-1
3- -5
3- -11
9- -17
Write an equation from slope-intercept form (y=mx+b ) from the table below.

Answer 1

To write an equation in slope-intercept form \(y = mx + b\), we first need to identify the slope (m) and the y-intercept (b) from the given data points.

The data points provided in the table appear to be:

\[
\begin{align*}
1 & \to 0 \\
-5 & \to 3 \\
-11 & \to 3 \\
-17 & \to 9 \\
\end{align*}
\]

Noticing that the x-values seem to be in the pattern of \(x = 0, 3, 3, 9\) and y-values \(y = 1, -5, -11, -17\).

However, let’s summarize it as follows from the corrected table:

\[
\begin{align*}
(0, -1) \\
(3, -5) \\
(3, -11) \\
(9, -17) \\
\end{align*}
\]

We can use the first two points \( (0, -1) \) and \( (3, -5) \) to calculate the slope.

1. **Calculate the Slope \(m\)**:

The slope \(m\) is calculated as follows:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{3 - 0} = \frac{-5 + 1}{3} = \frac{-4}{3} = -\frac{4}{3}
\]

2. **Find the y-intercept \(b\)**:

Since we have the point (0, -1), we can see that when \(x = 0\), \(y = -1\). Therefore, the y-intercept \(b\) is \(-1\).

3. **Write the Equation**:

Now that we have \(m\) and \(b\), we can write the equation in slope-intercept form:

\[
y = -\frac{4}{3}x - 1
\]

This is the equation that represents the relationship between \(x\) and \(y\) based on the points from the table.