Question

Using the graph, derived the equation of the line in slope intercept form coordinates are (0,-4) (1,-1)

Answer 1

To derive the equation of the line in slope-intercept form \(y = mx + b\) using the given coordinates \((0, -4)\) and \((1, -1)\), let's follow these steps:

1. **Identify the coordinates**:
- Point 1: \((0, -4)\)
- Point 2: \((1, -1)\)

2. **Calculate the slope (m)**:
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates:
\[
m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3
\]

3. **Use the slope and one of the points to find the y-intercept (b)**:
We can use the y-intercept from point (0, -4) directly:
Since the line passes through (0, -4), the y-intercept \(b\) is \(-4\).

4. **Write the equation in slope-intercept form**:
Now that we have \(m = 3\) and \(b = -4\), we can substitute these values into the slope-intercept formula:
\[
y = 3x - 4
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = 3x - 4}
\]