**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.
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`
To create a linear function (y=mx+b) and graph the line for the given set of data, we'll follow the steps:
Step 1: Find the slope (m) using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are two points.
Given points:
Point 1: (2, 1)
Point 2: (4, 2)
Using the slope formula:
m = (2-1) / (4-2)
m = 1/2
Step 2: Find the y-intercept (b) by substituting the slope (m) and one of the points (x, y) into the equation y = mx + b.
Using point (2, 1):
1 = (1/2)(2) + b
1 = 1 + b
b = 0
Step 3: Substitute the slope (m) and y-intercept (b) into the equation y = mx + b.
The equation becomes: y = (1/2)x + 0
Simplifying, y = (1/2)x
Step 4: Graph the line using the equation y = (1/2)x.
On a graph, plot the given points (2, 1), (4, 2), and (6, 3). Then, draw a straight line that passes through these points and extends in both directions.
The graph should show a line with a slope of 1/2 passing through the points (2, 1), (4, 2), and (6, 3).
To create a linear function and graph the line for the given set of data, let's follow these steps:
Step 1: Find the slope (m) using the slope formula:
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the given data points, choose any two pairs and assign them as (x1, y1) and (x2, y2).
For example, let's use the points (2, 1) and (4, 2):
m = (2 - 1) / (4 - 2)
m = 1/2
So the slope of the linear function is 1/2.
Step 2: Find the y-intercept (b):
Now, we have the slope (m) and a point (x, y) from the data. Let's choose any point from the given data, for example, (2, 1).
Using the slope-intercept form of a linear function (y = mx + b), substitute the values of x, y, and m:
1 = (1/2)(2) + b
1 = 1 + b
b = 1 - 1
b = 0
So the y-intercept (b) of the linear function is 0.
Step 3: Write the linear function:
With the slope (m = 1/2) and y-intercept (b = 0), we can write the linear function as:
y = (1/2)x + 0
y = (1/2)x
Step 4: Graph the line:
To graph the line, plot the given set of points on a coordinate plane and then draw a straight line that passes through those points.
The given data points are (2, 1), (4, 2), and (6, 3).
Plot these points on a graph and then draw a line passing through them using the linear function equation y = (1/2)x.
The graph will show a straight line passing through these points, representing the linear function y = (1/2)x.
Please note that the explanation provided is a step-by-step process for solving the problem.