Question

the table shows a linear relationship between the variables x and y.

x	y
7	21.5
11	31.5

what are the slope and y-intercept of 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)

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the first two points \((5, 16.5)\) and \((7, 21.5)\). Then \( m=\frac{21.5 - 16.5}{7 - 5}=\frac{5}{2} = 2.5\).

Step2: Find the y - intercept

The equation of a line is \( y=mx + b \), where \( b \) is the y - intercept. We know \( m = 2.5\) and we can use the point \((5,16.5)\). Substitute \( x = 5\), \( y=16.5\) and \( m = 2.5\) into the equation: \( 16.5=2.5\times5 + b \). Calculate \( 2.5\times5=12.5 \), then \( 16.5-12.5=b \), so \( b = 4\). The y - intercept is \((0,4)\) since when \( x = 0\), \( y=b\).

Answer:

slope 2.5, y - intercept (0,4)