Question

**Problem 3: Create a linear function (y=mx+b) and graph the line for the following set of data.

x | y
2 | 1
4 | 2
6 | 3

First, use the slope formula to find slope:
(y2-y1)/(x2-x1)

Then, put the slope (m), a 'y' point, and matching 'x' point into the formula y=mx+b.
Solve for 'b' (the y-intercept).
Next, put the slope and y-intercept into the y=mx+b form.
Lastly, use the y=mx+b to graph the line.

Answer 1

Well you already have the steps. :)

(1) First, use the slope formula to find slope:
m = (y2-y1) / (x2-x1)
From the table of values, let's take the first two points (2,1) and (4,2), and substitute them into the formula for slope:
m = (y2-y1) / (x2-x1)
m = (2 - 1) / (4 - 2)
m = 1/2

(2) Then, put the slope, a 'y' point, and matching 'x' point into the formula y = mx + b. Solve for 'b' (the y-intercept).
Let's take the first point (2,1), and we already have m so we can solve for b:
y = mx + b
1 = (1/2)(2) + b
1 = 1 + b
b = 0

(3) Next, put the slope and y-intercept into the y = mx + b form.
You have m = 1/2 and b = 0, therefore:
y = (1/2)x

(4) Graphs cannot be shown here so I'll leave the graphing to you. You already have the points (from the table of values), plot them on a graphing paper and connect them by drawing a straight line with an arrowhead on both ends.

Hope this helps~ `u`