We need to find the equation in slope-intersect form
[tex]y=mx+b[/tex]
of the given lines.
For the horizontal line, we can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,7) \\ (x_1,y_2)=(4,6) \end{gathered}[/tex]
the its slope (m) is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-7}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]
Then, the line equation has the form
[tex]y=-\frac{1}{4}x+b[/tex]
where b is the y-intercept. From the picture, we can see that the line crosses the y-axis at y=7, therefore, b=7. Then, the line equation for the horizontal line is
[tex]y=-\frac{1}{4}x+7[/tex]
Similarly, we can apply the same procedure for the other line. We can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,-2) \\ (x_2,\text{y}_2)=(4,6) \end{gathered}[/tex]
Then, the slope (m) of this line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-2)}{4-0}=\frac{6+2}{4}=\frac{8}{4}=2[/tex]
Then, the line equation has the form
[tex]y=2x+b[/tex]
Since this line crosses y-axis at y=-2 then b=-2. Hence, the equation is
[tex]y=2x-2[/tex]
In summary, the system of linear equations is:
[tex]\begin{gathered} y=-\frac{1}{4}x+7 \\ y=2x-2 \end{gathered}[/tex]
