Suppose that someone said that the equation connecting points (-1, 1) and (2, 3) is y=2/3x+ 5/3. This person wants to know whether the line represented by this equation will contain point (6, 9). Identify two ways by which this person can decide whether the graph of the equation contains the point.
1. see if the point (6,9) satisfies the equation
2. use (6,9) with one of the other points and see if you get the same equation
There are two ways by which this person can decide whether the graph of the equation contains the point (6, 9). Let's explore both methods:
Method 1: Substitution
The first method is to substitute the coordinates of the point (6, 9) into the equation and check if the equation holds true.
Step 1: Replace x with 6 and y with 9 in the equation y = (2/3)x + (5/3).
9 = (2/3)(6) + (5/3)
9 = 12/3 + 5/3
9 = 17/3
Step 2: Simplify the equation.
9 = 17/3
Since 9 is not equal to 17/3, the equation does not hold true when the point (6, 9) is substituted. This means that the line represented by the equation does not contain the point (6, 9).
Method 2: Graphical Representation
The second method is to plot the points (-1, 1), (2, 3), and (6, 9) on a graph and check if they all fall on the same line.
Step 1: Plot the three points on a graph.
Point (-1, 1)
Point (2, 3)
Point (6, 9)
Step 2: Draw a straight line passing through the points (-1, 1) and (2, 3) according to the equation y = (2/3)x + (5/3).
Step 3: Check if the point (6, 9) falls on the line.
By visual inspection, we can see that the point (6, 9) does not lie on the line.
Based on both methods, we can conclude that the line represented by the equation y = (2/3)x + (5/3) does not contain the point (6, 9).