The equation [tex]y = -0.04x + 12[/tex] gives the number of gallons of gas in your car, where [tex]x[/tex] is the number of miles driven.
a. Graph the equation.
b. Interpret the slope and y-intercept of the line.
Answer (3)
a. you can graph the equation by inputting numbers for x - i recommend the range from -3 to 3. this will give you a y value, and then both can be used as coordinates to plot points on a graph. These will outline your linear line.
b. the slope can be calculated by using the equation: change in y / change in x, or (y_1 - y_2) / (x_1 - x_2) where (x_1, y_1) and (x_2, y_2) are both points on the line.
the y intercept is the value of y when x = 0, or where the line crosses the x axis.
The graph is attached.
The negative slope means that the relation between variables is not directly proportional, that is, the more number of miles driven, less number of gallons of gas we have in our cars, this is an inverse proportion, while one increases, the other one decreases.
On the other hand, the *y-intercept *indicates the number of gallons of gas in the car when the car is not moving yet, that is, when the number of miles are zero. So, in this case, before the car moves, there are 12 gallons of gas in the car. ;
To graph y = − 0.04 x + 12 , plot points like the y-intercept (0, 12) and another point such as (100, 8), then connect them with a line. The slope of -0.04 indicates that the fuel decreases as miles increase, and the y-intercept shows 12 gallons of fuel when no miles are driven (x = 0). This highlights the relationship between driving distance and gasoline consumption.
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