Let's analyze the images and graphs to see why the equations provided are marked incorrect.

(b) $Q(t) = 6t$ - Incorrect

• From the graph, we see a straight line passing through the origin $(0,0)$ with a positive slope.
• By inspecting points like $(1, 6)$, the line rises 6 units for each 1 unit increase in $t$, indicating a slope of 6.
• However, the line does not pass through the origin as would be expected from the equation $Q(t) = 6t$. It appears that the correct equation might be something like $Q(t) = 6t + b$, where $b$ is the y-intercept.

(c) $y = 1x$ - Incorrect

• In this graph, the line has a negative slope and is decreasing.
• The provided equation $y = 1x$ (or $y = x$) suggests a slope of 1, which would result in an upward sloping line at a 45-degree angle.
• From the graph, it seems the slope is actually negative, and the equation should likely be of the form $y = -x + b$, indicating a negative slope.

Would you like further details on how to calculate the correct equations from the graphs?

Here are 5 related questions for deeper understanding:

1. How do you find the slope of a line from its graph?
2. How do you determine the y-intercept from a line's graph?
3. What is the difference between a positive and negative slope on a graph?
4. How would you rewrite a linear equation if the line does not pass through the origin?
5. What methods can be used to verify if an equation matches a graph?

Tip: Always check both the slope and the y-intercept when comparing equations to their corresponding graphs.