Question

Write an equation from slope-intercept form (

𝑦
=
𝑚
𝑥
+
𝑏
y=mx+b ) from the table below. Click Here for Help Video.

𝑥-𝑦
0- -3
5-2
10-7
15-12

Answer 1

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

Let's analyze the pairs from the table:

- \((0, -3)\)
- \((5, -2)\)
- \((10, -7)\)
- \((15, -12)\)

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

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

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

Let's choose two points from the table. We'll use \((0, -3)\) and \((5, -2)\):

\[
m = \frac{-2 - (-3)}{5 - 0} = \frac{-2 + 3}{5} = \frac{1}{5}
\]

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

We can use the y-intercept directly from the point \((0, -3)\). Here, when \(x = 0\), \(y = -3\), thus \(b = -3\).

### Step 3: Write the equation

Using the slope \(m = \frac{1}{5}\) and the y-intercept \(b = -3\), we can now write the equation:

\[
y = \frac{1}{5}x - 3
\]

### Conclusion

The equation in slope-intercept form from the provided table is:

\[
y = \frac{1}{5}x - 3
\]