The table shows a linear relationship between variables x and y

Question

X,Y
5, 16.5
7, 21.5
11, 31.5
What are the slope and y intercept for the linear relationship?

Remember, you can also enter this table of numbers in your Desmos calculator to find the slope and y-intercept.

After you enter the table of numbers, in the next entry, enter y1- mx1+b.

slope 2. y-intercept (0, 6.5)

slope -2. y-intercept (4.0)

slope -2.5, y-intercept (4.0)

slope 2.5. y-intercept (0.4)

Answer 1

To determine the slope and y-intercept from the given points in the linear relationship between x and y, we can follow these steps:

1. Identify two points from the table:

   • Point 1: (5, 16.5)
   • Point 2: (7, 21.5)

2. Calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points: \[ m = \frac{21.5 - 16.5}{7 - 5} = \frac{5}{2} = 2.5 \]

3. Now we have the slope \( m = 2.5 \). To find the y-intercept \( b \), we can use the slope-intercept form of the equation of a line \( y = mx + b \). We can substitute one of the points (let's use the first one, (5, 16.5)) into the equation: \[ 16.5 = 2.5(5) + b \] \[ 16.5 = 12.5 + b \] \[ b = 16.5 - 12.5 = 4.0 \]

Thus, the slope is \( 2.5 \) and the y-intercept is \( 4.0 \).

In conclusion:

• Slope: \( 2.5 \)
• Y-Intercept: \( 4.0 \)

The corresponding answer from your options would be:

• slope 2.5, y-intercept (4.0)