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Sagot :
The two points given are (125, 10) and (150, 9)
y = number of gallons (in tanks),
x = number of miles driven
[tex]\begin{gathered} x_1=125,y_1=10_{} \\ x_2=150,y_2=9_{} \end{gathered}[/tex]a. The rate of change = The slope =
[tex]\text{Slope =}\frac{y_2-y_{1_{}}}{x_2-x_1}=\frac{9-10}{150-125}=-\frac{1}{25}[/tex]So, the rate of change is -1/25 gallon/mile (or -0.04 gallon/mile)
b. The rate of change means the amount of gallon(s) used per mile driven.
c. y-intercept is the value of y when x = 0.
From the graph, we read that y = 15 gallons when x = 0
Thus, y-intercept is 15 gallons.
d. y-intercept means the number of gallons (in tank) when zero mile is driven.
e. The equation of the line-graph is given by;
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ \text{where x}_1=125 \\ y_1=_{}10 \\ y-10=-\frac{1}{25}(x-125) \\ \text{Clearing the bracket, we get} \\ y-10=-\frac{1}{25}x+5 \\ \text{Collecting like terms, we get} \\ y=-\frac{1}{25}x\text{ + 5+10} \\ \\ y=-\frac{1}{25}x\text{ + 15} \end{gathered}[/tex]Hence, the equation of the graph is y = - 0.04x + 15 or
[tex]y=-\frac{1}{25}x\text{ + 15}[/tex]
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