Question

Using the graph, derive the equation of the line in slope-intercept form.

y = 3x − 4

y = −3x − 4

y = 3x + 4




3x − y = 4

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b), we will analyze the options given, as they seem to represent different lines.

1. **Slope-Intercept Form:**
- The form \(y = mx + b\) indicates that \(m\) is the slope and \(b\) is the y-intercept.

2. **Given Options:**
- Option 1: \(y = 3x - 4\) (Slope = 3, Y-intercept = -4)
- Option 2: \(y = -3x - 4\) (Slope = -3, Y-intercept = -4)
- Option 3: \(y = 3x + 4\) (Slope = 3, Y-intercept = 4)
- Option 4: \(3x - y = 4\) which can be rearranged to \(y = 3x - 4\) (Slope = 3, Y-intercept = -4)

From the options, we see that the first and fourth equations provide the same line:

- **Using the Fourth Equation:**
To rearrange \(3x - y = 4\) into slope-intercept form:
\[
-y = -3x + 4
\]
\[
y = 3x - 4
\]

Depending on where the line crosses the y-axis and its slope (visualized on the graph), we would consider the correct lines based on the graph that corresponds to the presented options.

The final equation in slope-intercept form derived from the context provided is:

\[
y = 3x - 4
\]

If you have specific coordinate points or a visual to reference, please provide them for a more accurate analysis.