Question

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

y= ____ x+ _____

Answer 1

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

Using the points from the table, we can pick two points to calculate the slope \( m \). Let's use the points (-2, -7) and (2, 5).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Substituting in our selected points:

\[
m = \frac{5 - (-7)}{2 - (-2)} = \frac{5 + 7}{2 + 2} = \frac{12}{4} = 3
\]

Now that we have the slope \( m = 3 \), we can use one of the points to find the y-intercept \( b \). Let's use the point \( (0, -1) \) since it's already in the form of \( y = mx + b \):

Substituting \( x = 0 \) and \( y = -1 \):

\[
-1 = 3(0) + b \implies -1 = b
\]

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

\[
y = 3x - 1
\]

Thus, the equation is:

\[
y = 3x - 1
\]

So the final answer is:

y = **3** x + **(-1)** or just y = **3** x - **1**.