Question

the graph shows the distance a microcar travels at its top speed over time. write an equation for the distance the car travels, y, after x hours. y = 40x how can you write an equation for any proportional relationship with slope m? options: y = x/m, y = x + m, y = m/x, y = mx

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship has a graph that passes through the origin \((0,0)\) and can be represented by the equation \(y = mx\), where \(m\) is the slope (rate of change).

Step2: Analyze Options

• \(y=\frac{x}{m}\): Rearranged, \(x = my\), not a proportional relationship in the form of \(y\) in terms of \(x\) with slope \(m\).
• \(y=x + m\): This is a linear equation with \(y\)-intercept \(m\), not proportional (since proportional relationships have \(y\)-intercept \(0\)).
• \(y=\frac{m}{x}\): This is an inverse relationship, not proportional.
• \(y = mx\): This is the standard form for a proportional relationship with slope \(m\) (since when \(x = 0\), \(y = 0\), and the slope is \(m\)).

Answer:

\(y = mx\) (the option with \(y = mx\))