Question

deriving $y = mx + b$ continued
graphs
5
student answers
$y = 4x + 5$
6
$y = 40x + 20$
7
$y = 25x + 50$
8 explain one way you could know that the equation of a line is wrong without performing calculations.

Explanation:

One way is to check the y - intercept. The y - intercept (b in \(y = mx + b\)) is the value of y when \(x = 0\). Visually, we can look at the graph to see where the line crosses the y - axis. If the equation's b - value doesn't match the y - intercept from the graph, the equation is wrong. For example, in graph 5, the line crosses the y - axis at \(y = 4\), but the student's equation is \(y=4x + 5\) (where \(b = 5\)), so we can tell it's wrong by comparing the y - intercept from the graph and the equation.

Answer:

One way is to check the y - intercept (the value of \(y\) when \(x = 0\)) from the graph and compare it to the \(b\) - value in the equation \(y=mx + b\). If they don't match, the equation is wrong.