Question

Points and lie on the same line, as shown in the coordinate plane picture below and label each on you’re doing as,,.) What is the slope of the line passing through points and ? Show or explain all your work) Write the equation of the line passing through points and show or explain all your work) Points and are added to the coordinate plane and a new line, , is made. Describe the three possible solutions to the system of linear functions, and , made.

Answer 1

Given:

Points and lie on the same line, as shown in the coordinate plane picture

The coordinates of point J = (3, 3.5)

The coordinates of point K = (6, 5)

We will answer the following questions:

) What is the slope of the line passing through points and ?

The slope is given by the formula:

`slope=(rise)/(run)=(y_2-y_1)/(x_2-x_1)`

Substitute with the points J and K

`slope=(5-3.5)/(6-3)=(1.5)/(3)=(1)/(2)`

) Write the equation of the line passing through points and

The slope-intercept form of the equation is as follows

`y=mx+b`

where m is the slope, and (b) is the y-intercept

So, from (A) m = 1/2

As shown in the figure, b = y-intercept = 2

So, the equation of the line will be:

`y=(1)/(2)x+2`

) Points and are added to the coordinate plane and a new line, , is made. Describe the three possible solutions to the system of linear functions, , and , made.

So, there are 3 possible solutions:

First, the line LM has a different slope, so, it will be consistent independent system, the lines will intersect at one point

Second, The lines have the same slope and the same y-intercepts, the system will be a consistent dependent system the lines will be identical (the same line), there are infinite solutions

Third, the lines have the same slope but a different y-intercept, the lines will be parallel, there is no intersection between them so, there is no solution, it will be an inconsistent system.