Question

he graph below shows the distance, d, that Ian drives his car over time, t. The graph shows a line passing through (0, 0) and (1, 50). Rachel says she drives more slowly than Ian. Which equation can represent the distance Rachel drives over time? Responses d=60t d = 60 t d=70t d = 70 t d=50t d = 50 t d=40t

Answer 1

Ian's distance equation is
`\(d = 50t\)`. Rachel drives slower, roughly half Ian's speed, so her distance equation is
`\(d_{\text{Rachel}} = 25t\),` showing her distance over time.

If Ian's distance is represented by a linear equation passing through the points (0, 0) and (1, 50), we can find the equation using the slope-intercept form,
`\(y = mx + b\)` where
`\(m\)` is the slope and
`\(b\)` is the y-intercept.

Given the points (0, 0) and (1, 50):

Let's find the slope,
`\(m\)`, using the formula:

`\[m = \frac{{\text{change in }} y}{{\text{change in }} x} = \frac{{50 - 0}}{{1 - 0}} = \frac{{50}}{{1}} = 50\]`

Therefore, the slope of Ian's distance is
`\(m = 50\).`

Now that we have the slope, we can form the equation for Ian's distance,
`\(d\)`, over time,
`\(t\)`:

`\[d = 50t\]`

Rachel drives more slowly than Ian. If we assume Rachel's speed is half of Ian's speed, her equation for distance over time would be:

`\[d_{\text{Rachel}} = (1)/(2) * 50t = 25t\]`

Therefore, the equation representing the distance Rachel drives over time is
`\(d_{\text{Rachel}} = 25t\).`