Question

HELP ASAPPP

Part 1
Determine the x and y intercepts of the linear equation 3x-y-1=0. Use the intercepts to graph the line. On your graph label the pints that represent the x and y intercepts.

Part 2
Determine the slope and Y intercept of the linear equation 3X minus Y minus one equals zero use the slope and Y intercept to graph the line. On your graph, label the point that represents the Y intercept and one additional point found by applying the slope of the line.

Part 3
In the form of a paragraph, compare and contrast the methods used for graphing the linear equation 3x-y-1=0 in Parts 1 and 2.

Answer 1

Part 1)

The y-intercept is the point (0,-1)

The x-intercept is the point (1/3,0)

The graph in the attached figure N 1

Part 2) The graph in the attached figure N 2 (see the explanation)

Part 3) see the explanation

Explanation:

Part 1) Determine the x and y intercepts of the linear equation 3x-y-1=0. Use the intercepts to graph the line

we have

`3x-y-1=0`

step 1

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

`3(0)-y-1=0\\y=-1`

The y-intercept is the point (0,-1)

step 2

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

`3x-(0)-1=0\\x=(1)/(3)`

The x-intercept is the point (1/3,0)

step 3

To graph the line, plot the intercepts and join then

The graph in the attached figure N 1

Part 2) Determine the slope and Y intercept of the linear equation 3X minus Y minus one equals zero use the slope and Y intercept to graph the line. On your graph, label the point that represents the Y intercept and one additional point found by applying the slope of the line.

we have

`3x-y-1=0`

isolate the variable y

Adds y both sides

`y=3x-1`

This is the equation of the line in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=3\\b=-1`

so

The y-intercept is the point (0,-1)

Point and a slope to graph the line

the point is (0,-1)

the slope is m=3

Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

rise=3

run=1

so

To graph the line

1. Plot the point (0,-1).

2. From that point, count right 1 unit and up 3 unit and plot a second point.

(0+1,-1+3)

(1,2)

3. Draw a line through the two points

we have

(0,-1) and (1,2)

The graph in the attached figure N 2

Part 3) In the form of a paragraph, compare and contrast the methods used for graphing the linear equation 3x-y-1=0 in Parts 1 and 2

In the first method, we use the intercepts to plot the line (see the explanation part 1)

In the second method, we use the y-intercept and the slope in order to have two points and thus be able to graph the line (see the explanation Part 2)

By comparing and contrasting the two methods, we can see that the graph obtained is the same