Question

Write an equation in slope-intercept form ( y = mx+b ) from the table below.
x, y
-2 -7
-1 -4
0 -1
2 5

Answer 1

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

First, we can calculate the slope \( m \) using two points from the table. Let's use the points \((-2, -7)\) and \( (0, -1)\).

The formula for slope \( m \) is:

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

Using the points \( (x_1, y_1) = (-2, -7) \) and \( (x_2, y_2) = (0, -1) \):

\[
m = \frac{-1 - (-7)}{0 - (-2)} = \frac{-1 + 7}{0 + 2} = \frac{6}{2} = 3
\]

Now that we have the slope \( m = 3 \), we can now find the y-intercept \( b \). We can use one of the points for this. Using the point \( (0, -1) \):

Since the x-coordinate is 0, we can directly identify \( b \):

\[
b = -1
\]

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

\[
y = mx + b
\]
\[
y = 3x - 1
\]

Thus, the equation in slope-intercept form that represents the relationship from the given table is:

\[
y = 3x - 1
\]