Question

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

x	-2	-1	0	1	2
y	-7	-4	-1	2	5

find the y-intercept and slope of the functions graph, and find the equation for the function.
y-intercept:
slope:
equation:

Explanation:

Step1: Find y-intercept

The y-intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = -1 \). So the y-intercept is \( -1 \).

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, e.g., \( (0, -1) \) and \( (1, 2) \). Then \( m=\frac{2 - (-1)}{1 - 0}=\frac{3}{1}=3 \).

Step3: Find the equation

The slope - intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know \( m = 3 \) and \( b=-1 \), so the equation is \( y = 3x-1 \).

Answer:

y - intercept: \(-1\)
slope: \(3\)
equation: \(y = 3x - 1\)