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)
+118609 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
