Question

the table shows a set of points on a line.

x	0	2	4	6
y	3	4	5	6

what is the slope of the line?
options: -2, $-\frac{1}{2}$, $\frac{1}{2}$, 2

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Select two points from the table

Let's take the points \((0, 3)\) and \((2, 4)\) (we can choose any two points from the table, e.g., \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(2,4)\)).

Step3: Substitute into slope formula

Substitute \( x_1 = 0 \), \( y_1 = 3 \), \( x_2 = 2 \), \( y_2 = 4 \) into the formula: \( m=\frac{4 - 3}{2 - 0}=\frac{1}{2} \). We can verify with other points, e.g., \((2,4)\) and \((4,5)\): \( m=\frac{5 - 4}{4 - 2}=\frac{1}{2} \), or \((4,5)\) and \((6,6)\): \( m=\frac{6 - 5}{6 - 4}=\frac{1}{2} \).

Answer:

\(\frac{1}{2}\)