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

First, let's extract the coordinates from the table:

1. (-2, -7)
2. (-1, -4)
3. (0, -1)
4. (1, 2)
5. (2, 5)

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

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

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

Using the points (0, -1) and (1, 2):

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

### Step 2: Use the Slope and a Point to Find the y-Intercept (b)

Using the slope and one of the points (we can use (0, -1) because it gives us b directly):

\[
y = mx + b
\]
Substituting the point (0, -1) into the equation:

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

### Step 3: Write the Final Equation

Now we have the slope (m = 3) and the y-intercept (b = -1). Thus, the equation in slope-intercept form is:

\[
y = 3x - 1
\]

So the final answer is:

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