Question

9. The table represents some points on a linearfunction which situation can be modeled by thisfunction?X35813A The cost of buying x number of concert tickets for$76 eachB. The number of pages y that can be read in 76minutesc. The number of gallons of fuel x that can be used toD. The amount of money spent from a stingsaccount with y dollars

Answer 1

We can write the equation of the line from the table

The general equation of a line is

`y=mx+b`

where m is the slope and b the y-intercept, the we need to find m and b to replace on the general equation and obtain the function of the line

Slope (m)

We use the formula of the slope

`m=(y2-y1)/(x2-x1)`

where (x2,y2) is a right point from (x1,y1), I can use any pair of points of the table, on this case I will use (3,228) and (7,532)

where (3,228) is (x1,y1) and (7,532) is (x2,y2)

then replacing

`\begin{gathered} m=(532-228)/(7-3) \\ \\ m=(304)/(4) \\ \\ m=76 \end{gathered}`

The slope is 76

y-intercept

We repalce the slope on the general equation

`y=76x+b`

then we replace any point (x,y) for example (11,836)

`836=76(11)+b`

simplify

`836=836+b`

and solve for b

`\begin{gathered} b=836-836 \\ b=0 \end{gathered}`

Final equation

replace values of m and b on the general equation to obtaion our linear function

`\begin{gathered} y=76x+0 \\ \\ \\ y=76x \end{gathered}`

then right option is first, because multiply a number of something by the value of each(76)