Question

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

x	-2	-1	0	1	2
y	-12	-10	-8	-6	-4

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 \(x=0\), \(y=-8\). So the y - intercept \(b=-8\).

Step2: Calculate the slope

The slope \(m\) of a linear function is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table, for example, \((x_1,y_1)=(-2,-12)\) and \((x_2,y_2)=(-1,-10)\). Then \(m=\frac{-10 - (-12)}{-1-(-2)}=\frac{-10 + 12}{-1 + 2}=\frac{2}{1}=2\). We can check with another pair of points, say \((0,-8)\) and \((1,-6)\). \(m=\frac{-6-(-8)}{1 - 0}=\frac{-6 + 8}{1}=\frac{2}{1}=2\). So the slope \(m = 2\).

Step3: Find the equation of the line

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 that \(m = 2\) and \(b=-8\), so the equation is \(y=2x-8\).

Answer:

y - intercept: \(-8\)
slope: \(2\)
equation: \(y = 2x-8\)