Use the ordered pairs to write a function rule. Give the rule in the slope-intercept form. (–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5)

Use the ordered pairs to write a function rule. Give the rule in the slope-intercept form.

(–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5)

 

 

The last row was added later as a check,

x	-12	-1	5	8
y	1.5	-1.25	-2.75	-3.5
check
y=-x/4  - 1.5	--12/4-1.5=1.5	--1/4-1.5=-1.24	-5/4-1.5=-2.75	-8/4-1.5=-3.5

 

You are told to give the rule in gradient and y intercept form so that immediately says it is a line and will be written in  the form   y=mx+b

 

Choose ANY 2 points to find the gradient m.  I'll use the last 2

$m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-3.5-\;-2.75}{8-5}=\frac{-0.75}{3}=-0.25$

 

y = -0.25x + b

 

Now sub in any of the points to get the y intercept.  I'll use (-1, -1.25)

-1.25=-0.25*-1+b

-1.25=  0.25 +b

-1.25-0.25=b

b = -1.5

 

y = -0.25x - 1.5

or

y=-x/4  - 1.5

 

I have checked each of the points on the table above to make sure that the equation works for all points

A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Explain your reasoning.

slope of the line

equation of the line

y-intercept

slope of a line perpendicular to the given line