Question

Analyze the graph. Use the triangle to find the slope, m, of the line.


The side of the triangle starts at -4 and ends 2 units above her. The pointy part of the triangle ends at 3
What is the slope, m, of the line? Enter your answer as a decimal. Round to the nearest hundredth.

Answer 1

To find the slope \( m \) of a line using the triangle method, we need to determine the rise (change in y) and the run (change in x).

From your description:
- The starting point on the x-axis is at \( x = -4 \).
- The vertical rise is described as "2 units above her" (which we can interpret as a rise of 2 units).
- The peak of the triangle (end point) is at \( x = 3 \).

1. Determine the run (change in x):
\[
\text{Run} = 3 - (-4) = 3 + 4 = 7
\]

2. Determine the rise (change in y):
Since it rises 2 units,
\[
\text{Rise} = 2
\]

3. Calculate the slope \( m \):
\[
m = \frac{\text{Rise}}{\text{Run}} = \frac{2}{7} \approx 0.285714
\]

Rounding to the nearest hundredth:
\[
m \approx 0.29
\]

Thus, the slope \( m \) of the line is \( \boxed{0.29} \).