Question

question
the table below represents a linear function. identify the slope of the function.

x	y
0	3
4	10
8	17
12	24

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through 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: Choose two points from the table

Let's take the first two points \((0, 3)\) and \((4, 10)\). Here, \( x_1 = 0 \), \( y_1 = 3 \), \( x_2 = 4 \), \( y_2 = 10 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{10 - 3}{4 - 0}=\frac{7}{4} \). We can verify with another pair of points, say \((4, 10)\) and \((8, 17)\). Then \( m=\frac{17 - 10}{8 - 4}=\frac{7}{4} \), and with \((8, 17)\) and \((12, 24)\), \( m=\frac{24 - 17}{12 - 8}=\frac{7}{4} \). So the slope is consistent.

Answer:

\(\frac{7}{4}\)