Identify the Equation: Matching Functions to Table Data

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

00:06 We'll use the formula to find the function graph's slope

00:11 We'll substitute appropriate values according to the given data and solve to find the slope

00:21 This is the slope of the graph

00:30 We'll use the linear equation

00:34 We'll substitute appropriate values and solve for B

00:44 This is the value of B

00:49 We'll construct the linear equation using the values we found

00:54 And this is the solution to the question

Step-by-Step Solution

To determine the corresponding equation for the given table, follow these steps:

Step 1: Confirm the linearity of the data by calculating the slope, $m$ , using consecutive data points:
- Between points $(-2, 0)$ and $(0, 1)$ , the slope is $m = \frac{1 - 0}{0 - (-2)} = \frac{1}{2}$ .
- Between points $(0, 1)$ and $(2, 2)$ , the slope is $m = \frac{2 - 1}{2 - 0} = \frac{1}{2}$ .
- Confirm the same slope $m = \frac{1}{2}$ for remaining pairs $(2, 2)$ and $(4, 3)$ , $(4, 3)$ and $(6, 4)$ .
Step 2: Use one point, such as $(0, 1)$ , to find the y-intercept, $b$ , knowing the slope $m = \frac{1}{2}$ :
- Use the slope-intercept form: $y = mx + b$ . Substituting $(0, 1)$ , gives $1 = \frac{1}{2}(0) + b$ , implying $b = 1$ .
Step 3: Formulate the equation: Given $m = \frac{1}{2}$ and $b = 1$ , the linear function is:
- $y = \frac{1}{2}x + 1$ .
Step 4: Compare with provided choices:

The equation $y = \frac{1}{2}x + 1$ matches choice 4. Therefore, the correct equation corresponding to the table is $y = \frac{1}{2}x + 1$ .