Question

a table of values of a linear function is shown below.
x | -3 | 0 | 3 | 6
y | 1 | -2 | -5 | -8
find the y-intercept and slope of the functions graph.
y-intercept:
slope:

Explanation:

Step1: Find y-intercept

The y-intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y=-2 \). So the y-intercept is \(-2\).

Step2: Calculate slope

The slope \( m \) of a linear function is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points, say \( (x_1,y_1)=(0, - 2) \) and \( (x_2,y_2)=(3,-5) \). Then \( m=\frac{-5 - (-2)}{3 - 0}=\frac{-5 + 2}{3}=\frac{-3}{3}=-1 \). We can check with another pair, like \( (x_1,y_1)=(3,-5) \) and \( (x_2,y_2)=(6,-8) \). \( m=\frac{-8-(-5)}{6 - 3}=\frac{-8 + 5}{3}=\frac{-3}{3}=-1 \). So the slope is \(-1\).

Answer:

y - intercept: \(-2\)
slope: \(-1\)