Answer
[tex]y=-2x+14[/tex]
Explanation
The general equation in slope-intercept form is
[tex]\begin{gathered} y=mx+c \\ \text{Where;} \\ m\text{ is the slope} \\ \text{c is the y-intercept} \end{gathered}[/tex]
From the graph,
The coordinates of the first yellow point (x₁, y₁) = (4, 6)
The coordinates of the second yellow point (x₂, y₂) = (7, 0)
Now, slope, m =
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-6}{7-4}=-\frac{6}{3} \\ m=-2 \end{gathered}[/tex]
The equation becomes y = -2x + c
To get c, use the coordiates (4, 6), substitute x = 4 and y = 6 into the above equation.
This implies
[tex]\begin{gathered} 6=-2(4)+c \\ 6=-8+c \\ c=6+8 \\ c=14 \end{gathered}[/tex]
Therefore, the equation in slope-intercept form is
[tex]y=-2x+14[/tex]
