Question

The graph shows the number of gallons of white paint that were mixed with gallons of blue paint in various diffrent ratios:

Answer 1

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

`y=mx+b`

where m is the slope and b the y-intercept. The slope can be computed as

`m=(y_2-y_1)/(x_2-x_1)`

where,

`\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(6,12) \end{gathered}`

By substituying these values into m, we have

`m=(12-4)/(6-2)`

hence,

`\begin{gathered} m=(8)/(4) \\ m=2 \end{gathered}`

the form of the line equation is

`y=2x+b`

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):

`\begin{gathered} 4=2(2)+b \\ 4=4+b \\ b=0 \end{gathered}`

Thefore, the line equation is

`y=2x`

Hence, the number of galons when we mix 1 gallon of blue pain is

`\begin{gathered} y=2(1) \\ y=2 \end{gathered}`

in other words, for 1 gallon of blue paint we must have 2 gallons of white paint