From the graph, we can note that the points are in a line.
Hence, we must find the line equation for these points.
The general form of the straigh line equation is
[tex]y=mx+b[/tex]
where m is the slope and b the y-intercept. The slope can be computed as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where,
[tex]\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(6,12) \end{gathered}[/tex]
By substituying these values into m, we have
[tex]m=\frac{12-4}{6-2}[/tex]
hence,
[tex]\begin{gathered} m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]
the form of the line equation is
[tex]y=2x+b[/tex]
where x is the blue paint and y the white paint.
In order to find b, we can substitute one point into the above equation. For instance, the point
(2,4):
[tex]\begin{gathered} 4=2(2)+b \\ 4=4+b \\ b=0 \end{gathered}[/tex]
Thefore, the line equation is
[tex]y=2x[/tex]
Hence, the number of galons when we mix 1 gallon of blue pain is
[tex]\begin{gathered} y=2(1) \\ y=2 \end{gathered}[/tex]
in other words, for 1 gallon of blue paint we must have 2 gallons of white paint
