Question

4.1.8Question HelpoUse the graph to the right to complete parts a through c below.Ау6-4(2, 2)2(-2,0)a. Describe the solution set for the system of equations that consists of the equation of the line shown and y =2x-3SA. The solution set is (Type an ordered pair.)OB. There are infinitely many solutions,O C. There is no solutionClick to select and enter your answer(s) and then click Check AnswerpartsremainingClear AllCheck Answer

Answer 1

To solve the problem, define the system of equation and solve it.

The first step to do it is to find the equation of the line drawn. Find the slope using the given points (-2,0) and (2,2).

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{2-0}{2-(-2)}=\frac{2}{4}=\frac{1}{2} \end{gathered}$

Use one of the points (-2,0) and the slope to find the equation of the line using the point slope formula:

$\begin{gathered} y-0=\frac{1}{2}(x-(-2)) \\ y=\frac{1}{2}x+1 \end{gathered}$

Once found the equation of the line drawn, it is not even necessary to solve the system to answer the problem.

As both equations have the same slope, they are parallel lines, which means they will not intercept each other at any point. In other words, the system does not have a solution.

The correct answer is C. There is no solution.