Question

Write a system of equations that represent the graph .

Answer 1

To write an equation for the lines of the graph, we have to find the slope and the y-intercept of each line.

The y-intercept can be find as the value of y when the line intersects the y-axis.

For company L, that intersects at (0,10), the y-intersect is y(0)=10.

For company K, that intersects at (0,5). the y-intersect is y(0)=5.

The slope can be find using two points of the line.

For Company L we will use points (0,10) and (20,15). Then, we calculate the slope as:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-10}{20-0}=\frac{5}{20}=0.25$

For Company K, the points will be (0,5) and (20,15), and the slope will be calculated as:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-5}{20-0}=\frac{10}{20}=0.5$

With the slope and y-intercept we can write the equation of each line in slope-intercept form.

For Company L, with slope m=0.25 and y-intercept b=10 we will have:

$\begin{gathered} y=mx+b \\ y=0.25x+10 \end{gathered}$

For Company K, with slope m=0.5 and y-intercept b=5, we will have:

$y=0.5x+5$

Answer:

The system of equations will be:

Company L: y=0.25x+10

Company K: y=0.5x+5