Question

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

(1 point)
Responses

y=3x−4
y equals 3 x minus 4

y=−3x−4
y equals negative 3 x minus 4

y=3x+4
y equals 3 x plus 4

3x−y=4

Answer 1

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

Without the graph, I'll guide you through the process instead:

1. **Find Slope (m)**: The slope is calculated as the change in y over the change in x (rise/run). Look for two clear points on the line; use their coordinates to determine the slope.

- For example, if the line passes through the points (0, 4) and (1, 7), the slope would be:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 4}{1 - 0} = \frac{3}{1} = 3
\]

2. **Identify Y-intercept (b)**: This is the point where the line crosses the y-axis (x = 0). Using the example above, the y-intercept is 4.

3. **Write the equation**: Substitute the slope and y-intercept into the slope-intercept form:
\[
y = mx + b \quad \Rightarrow \quad y = 3x + 4
\]

If you provide more specific details based on the graph or the characteristics of the line, I can help you arrive at the exact equation from the provided options. Based on the choices given, if the identified slope is 3 and the y-intercept is 4, the correct answer would be:

**y = 3x + 4**.