Determine the Equation from the Table: Function Matching Challenge

Video Solution

Solution Steps

00:00 Find the appropriate equation for the function in the table

00:03 We want to find the slope of the graph

00:07 We'll use the formula to find the slope of a function graph

00:10 We'll substitute appropriate values according to the data and solve to find the slope

00:19 This is the slope of the graph

00:28 Let's take a point on the graph

00:33 We'll use the straight line equation

00:36 We'll substitute appropriate values and solve to find B

00:45 This is the value of B (intersection point with Y-axis)

00:51 Let's compose the straight line equation using the values we found

00:56 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Analyze the pattern of the given table. Notice that the increase in $Y$ for each increase of 2 in $X$ is 2, indicating a slope of 1.
Step 2: Choose a likely linear equation from the provided options.
Step 3: Verify which equation accurately represents all the data points.

Let's verify the equation $y = x + 1$ with all pairs:

For $X = -3$ , calculate $Y = (-3) + 1 = -2$ . This matches the $Y$ -value in the table.
For $X = -1$ , calculate $Y = (-1) + 1 = 0$ . This too matches the $Y$ -value.
For $X = 1$ , calculate $Y = 1 + 1 = 2$ . Again, this matches.
For $X = 3$ , calculate $Y = 3 + 1 = 4$ . This matches as well.
For $X = 5$ , calculate $Y = 5 + 1 = 6$ . Finally, this matches too.

Each of the calculated $Y$ -values using $y = x + 1$ aligns with the respective $Y$ -values from the table.

Therefore, the correct equation that represents the function is $y = x + 1$ .