Determine the Corresponding Equation from Tabular Function Data
Question
Which of the following equations corresponds to the function represented in the table?
Video Solution
Solution Steps
00:00Find the appropriate equation for the function in the table
00:03We want to find the slope of the graph
00:06We'll use the formula to find the function graph slope
00:10We'll substitute appropriate values according to the data and solve to find the slope
00:20This is the graph's slope
00:27Let's take a point on the graph
00:32We'll use the linear equation
00:37We'll substitute appropriate values and solve for B
00:46This is the value of B (the Y-axis intercept)
00:49We'll construct the linear equation using the values we found
00:55And this is the solution to the question
Step-by-Step Solution
To determine the equation corresponding to the values in the table, let's analyze the relationship between X and Y:
Step 1: Check the change in Y with respect to X. The values show that each time X increases by 1, Y increases by 1, indicating a consistent change.
Step 2: Calculate the slope m.
Since the change is constant:
Δy/Δx=1/1=1.
Thus, the slope m=1.
Step 3: Determine the y-intercept b.
When X is 0, Y is -2. Thus, b=−2.
Step 4: Formulate the equation.
Using the slope-intercept form, y=mx+b, where m=1 and b=−2, the equation of the line is
y=x−2.
Verification with the table:
- Substituting X=−2 yields Y=−2−2=−4, which matches the table.
- Similarly, substituting other values confirms consistency. Hence, this confirms our linear equation.
The corresponding equation for the function represented in the table is therefore y=x−2.