Question

what is the equation of the line?
options: ( y = \frac{1}{70}x ), ( y = \frac{1}{35}x ), ( y = 35x ), ( y = 70x )
(chart: x - time (h), y - distance (mi); line passes through origin and other points)

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0,0)\) and we can find another point. Let's take when \(x = 8\) (time in hours), what is \(y\) (distance in miles)? From the graph, when \(x = 8\), \(y = 560\) (since the distance is 560 mi at 8 h).

Step2: Calculate the slope \(m\)

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0,0)\) and \((8,560)\), we have \(m=\frac{560 - 0}{8 - 0}=\frac{560}{8} = 70\).

Step3: Write the equation of the line

The equation of a line in slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Since the line passes through the origin \((0,0)\), \(b = 0\). So the equation is \(y = 70x\).

Answer:

\(y = 70x\)