Question

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

Answer 1

To derive the equation of the line that passes through the points (0, 1) and (1, -4), we can follow these steps:

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

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

\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

3. **Use the slope-intercept form**:
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \(m\) is the slope and \(b\) is the y-intercept. We already know the slope \(m = -5\).

4. **Find the y-intercept (b)**:
Since we have the point (0, 1), we can directly identify the y-intercept from this point. When \(x = 0\), \(y = 1\), which means:
\[
b = 1
\]

5. **Write the equation**:
Substituting the values of \(m\) and \(b\) into the slope-intercept form:
\[
y = -5x + 1
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = -5x + 1}
\]