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

Answer 1

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

The points provided are:
- (-2, -7)
- (-1, -4)
- (0, -1)
- (1, 2)
- (2, 5)

### Step 1: Calculate the slope (m)

The slope \( m \) can be calculated using the formula:

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

We can use any two points from the table. Let's use the points (0, -1) and (1, 2):

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

### Step 2: Determine the y-intercept (b)

The y-intercept is the value of y when x = 0. From the table, when \( x = 0 \), \( y = -1 \). Therefore, \( b = -1 \).

### Step 3: Write the equation

Now that we have the slope and the y-intercept, we can write the equation in slope-intercept form:

\[
y = 3x - 1
\]

Thus, the equation representing the data in the table is:

\[
\boxed{y = 3x - 1}
\]