Question

a table of values of a linear function is shown below.

x	0	1	2	3
y	4	-2	-8	-14

find the slope and y-intercept of the functions graph.
slope:

y-intercept:

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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, say \((0, 4)\) and \((1, -2)\).

Step2: Calculate slope

Substitute \( x_1 = 0, y_1 = 4, x_2 = 1, y_2=-2 \) into the slope formula: \( m=\frac{-2 - 4}{1 - 0}=\frac{-6}{1}=-6 \).

Step3: Find y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 4 \). So the y - intercept is 4.

Answer:

slope: \(-6\)
y - intercept: \(4\)