Question

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

Answer 1

To find the equation in slope-intercept form (y = mx + b) from the given points, we'll first identify the points from the table based on the values you've provided:

```
x | y
---------
-2 | -7
-1 | -4
0 | -1
1 | 2
2 | 5
```

Next, we'll use two points to find the slope (m) of the line. Let's use the points (0, -1) and (1, 2):

1. **Calculate the slope (m)**:

The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using (0, -1) as (x₁, y₁) and (1, 2) as (x₂, y₂):
\[
m = \frac{2 - (-1)}{1 - 0} = \frac{2 + 1}{1} = \frac{3}{1} = 3
\]

2. **Use the slope and one point to find the y-intercept (b)**:

We can use the point (0, -1) to find b:
\[
y = mx + b
\]
Substituting in the values from the point (0, -1):
\[
-1 = 3(0) + b \implies -1 = b
\]

3. **Write the equation**:

Now that we have the slope and the y-intercept, we can write the equation:
\[
y = 3x - 1
\]

Thus, the equation in slope-intercept form is:
\[
y = 3x - 1
\]