The function can be expressed as an equation, a graph, or a table of values.
Equation: y+5=2/5(x-12) Graph:
Table:
x
y
(x,y)
12
-5
(12,-5)
17
-3
(17,-3)
22
-1
(22,-1)
Practice makes perfect
The exercise only calls for us to represent the function in two other ways. We will here also demonstrate a third representation.
Equation
We are told that the function has a slope of 25 and that it passes through the point ( 12, -5). Using this information, we can write our function as an equation in point-slope form.
y- y_1&= m(x- x_1)
&⇓
y-( -5)&= 2/5(x- 12)
Let's simplify this equation by using that subtraction of a negative can be written as an addition.
y-(-5)&=2/5(x-12)
&⇓
y+5&=2/5(x-12)
Graph
Another way to represent this function is by graphing it on a coordinate plane. We have the point ( 12, - 5) and a slope of 25. Recall that the slope is the change in y divided by the change in x.
m= 2/5
⇓
Δ y/Δ x= 2/5
We will now first plot the point ( 12, - 5). Then we will, as indicated by the slope, take a step of 5 units to the right and 2 units up to find a second point.
By drawing a line through the points we have our graph.
Table of Values
Yet another way to represent our function is by using a table of values. If one point and the slope is known we can make a rule for finding more points by using that the slope 2 5 can be written as change in y divided by change in x.
Δ y/Δ x=2/5
A new point can be found by adding 5 to the x-coordinate and 2 to the y-coordinate of the known point.
x_1+ Δ x = x_2 ⇒ x_1+ 5 = x_2
y_1+ Δ y = y_2 ⇒ y_1+ 2 = y_2
When a new point has been found, this second point can be used to find a third point, and so on. Let's create our table by starting at the given point ( 12, - 5). We will use the rule twice, making a table of values with three ordered pairs.
