Question

which is the equation of the line represented in the graph? (1 point) \\(\bigcirc\\ y = \frac{40}{3}x + \frac{140}{3}\\) \\(\bigcirc\\ y = \frac{3}{140}x - \frac{7}{2}\\) \\(\bigcirc\\ y = \frac{40}{3}x + 50\\) \\(\bigcirc\\ y = \frac{140}{3}x + \frac{40}{3}\\)

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using points (1, 60) and (7, 140):
$m = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3}$

Step2: Use point - slope form to find the equation

Point - slope form is $y - y_1 = m(x - x_1)$. Using point (1, 60) and $m=\frac{40}{3}$:
$y - 60 = \frac{40}{3}(x - 1)$
Expand: $y - 60 = \frac{40}{3}x - \frac{40}{3}$
Add 60 to both sides: $y = \frac{40}{3}x - \frac{40}{3}+60$
Convert 60 to thirds: $60=\frac{180}{3}$, so $y = \frac{40}{3}x+\frac{140}{3}$

Step3: Check with the other point (7, 140)

Plug $x = 7$ into $y=\frac{40}{3}x+\frac{140}{3}$:
$y=\frac{40}{3}(7)+\frac{140}{3}=\frac{280 + 140}{3}=\frac{420}{3}=140$, which matches the point (7, 140).

Answer:

$y=\frac{40}{3}x+\frac{140}{3}$ (the first option)