Question

Which system is represented by the graph?

Answer 1

pair of lines   ...............................................................

Answer 2

Answer:

$\left \{ {{y-5x=-2} \atop {y-5x=-4}} \right.$

Step-by-step explanation:

The given graph shows a system of equation that doesn't have any solutions, because lines are parallel.

However, we can find the system. First we have to find the equation of each line. To do so, we need to find the slope and then use the point-slope formula which is gonna give us the equation.

Line 1.

First we need to use to points. The left line is gonna be Line 1, which points are (0,-2) and (1,3). Let's find the slope

$m_{1} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} }=\frac{3-(-2)}{1-0}=\frac{3+2}{1}=5$

Then, we use the point-slope formula

$y-y_{1} =m(x-x_{1} )\\y-(-2) =5(x-0)\\y+2=5x\\y=5x-2$

Line 2.

We apply the same process to find the equation of Line 2, which is the right line. The points we are gonna use are (0,-4) and (1,1).

$m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }=\frac{1-(-4)}{1-0}=\frac{1+4}{1}=5$

Then, we use the point-slope formula

$y-y_{1} =m(x-x_{1} )\\y-(-4)=5(x-0)\\y+4=5x\\y=5x-4$

Now, we use the general expression of each equation

$y-5x=-2$

$y-5x=-4$

Therefore, the system is

$\left \{ {{y-5x=-2} \atop {y-5x=-4}} \right.$