To find the equation of the line given the points (7, 140) and (1, 60), we start by calculating the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let (x₁, y₁) = (7, 140) and (x₂, y₂) = (1, 60). Plugging in the values:
\[ m = \frac{60 - 140}{1 - 7} = \frac{-80}{-6} = \frac{80}{6} = \frac{40}{3} \]
Now that we have the slope \( m = \frac{40}{3} \), we can use the point-slope form of the equation of the line, which is:
\[ y - y_1 = m(x - x_1) \]
Using point (7, 140):
\[ y - 140 = \frac{40}{3}(x - 7) \]
Distributing \( \frac{40}{3} \):
\[ y - 140 = \frac{40}{3}x - \frac{40}{3} \cdot 7 \] \[ y - 140 = \frac{40}{3}x - \frac{280}{3} \]
Adding 140 to both sides to isolate \( y \):
\[ y = \frac{40}{3}x + 140 - \frac{280}{3} \]
Converting 140 to thirds:
\[ 140 = \frac{420}{3} \]
Now substituting this into the equation:
\[ y = \frac{40}{3}x + \frac{420}{3} - \frac{280}{3} \] \[ y = \frac{40}{3}x + \frac{140}{3} \]
The equation of the line is:
\[ y = \frac{40}{3}x + \frac{140}{3} \]
This is consistent with the response "𝑦 = 40/3 𝑥 + 140/3".
Thus, the correct answer is:
y = 40/3x + 140/3.