Question

Here is a graph of the equation 2x - 3y = 15.Are the points (1.5, -4f) and (4, -4) solutions to the equation? Explain or show how you know.

Answer 1

To know if a point is a solution to an equation, we have to evaluate the x-entry of the point at the equation and if the result is the y-entry of the point, then it is a solution, otherwise, it is not a solution.

Answer:

Evaluating the given equation at x=1.5 and solving for y we get:

$\begin{gathered} 2(1.5)-3y=15, \\ 3-3y=15, \\ 3-15=3y, \\ -12=3y, \\ -\frac{12}{3}=y, \\ -4=y\text{.} \end{gathered}$

Therefore, point (1.5,-4) is a solution to the given equation.

Now, since for each y there is only one x, then the point (4,-4) cannot be a point on the line, therefore (4,-4) is not a solution to the given equation.