Question

Here is a graph of the equation 2y - x = 1. Are the points (0, 1/2) and (-7,-3) solutions to the equation?

Answer 1

Step 1:

To test if a point is a solution to the equation of a line, the point must lie on the line. When substituting the x value of the point, you must get the y value of the point.

Step 2:

Write the equation of the graph.

`2y\text{ - x = 1}`

Step 3:

Let test for points (0, 1/2) and (-7, -3)

`\begin{gathered} \text{For (0, }(1)/(2)) \\ \text{Let find y when x = 0} \\ 2y\text{ - x = 1} \\ 2y\text{ - 0 = 1} \\ 2y\text{ = 1} \\ y\text{ = }(1)/(2) \\ \text{Hence point (0 , }(1)/(2))\text{ is a solution.} \end{gathered}`

Next, let test for points (-7, -3)

`\begin{gathered} \text{when x = -7} \\ \text{Let find y} \\ 2y\text{ - (-7) = 1} \\ 2y\text{ + 7 = 1} \\ 2y\text{ = 1 - 7} \\ 2y\text{ = -6} \\ y\text{ = }(-6)/(2) \\ y\text{ = -3} \\ \text{Hence point (-7, -3) is a solution.} \end{gathered}`

Yes, the two points (0, 1/2) and (-7, -3) are solutions to the equation.

You know because both points lie on the line.