Question

Using the graph, derive the equation of the line in slope-intercept form (3,1) (0,-1)

Answer 1

To derive the equation of the line in slope-intercept form \(y = mx + b\), you need to determine the slope \(m\) and the y-intercept \(b\).

1. **Calculate the slope (\(m\)):**
The formula for the slope 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 \((3, 1)\) and \((0, -1)\):
\[
(x_1, y_1) = (3, 1) \quad \text{and} \quad (x_2, y_2) = (0, -1)
\]
Plugging in the coordinates:
\[
m = \frac{-1 - 1}{0 - 3} = \frac{-2}{-3} = \frac{2}{3}
\]

2. **Find the y-intercept (\(b\)):**
The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, -1)\), we can see that the y-intercept \(b = -1\).

3. **Write the equation in slope-intercept form:**
Now that we have \(m = \frac{2}{3}\) and \(b = -1\), we can write the equation of the line:
\[
y = \frac{2}{3}x - 1
\]

So, the equation of the line in slope-intercept form is:
\[
y = \frac{2}{3}x - 1
\]