Question

question 8
all work for this question must be shown on the cap #3 worksheet!
a car manufacturer provided information about two different car models.
car a (graph: x-axis gas (gallons), y-axis distance (miles), line through points) car b (table: gas (gallons) 0,3,5,7,10; distance (miles) 0,60,100,140,200)
part a:
write the equation that represents the distance y (in miles) that car a travels with x gallons of gas.
your answer

Explanation:

Step1: Determine the type of function

The graph for Car A is a straight line passing through the origin, so it represents a proportional relationship, which can be modeled by the equation \( y = mx \), where \( m \) is the slope (rate of change).

Step2: Calculate the slope (m)

To find the slope, we can use two points from the graph. Let's use the points \((2, 50)\) and \((4, 100)\) (we can also use other points like \((6, 150)\), etc.). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Substituting the values: \( m=\frac{100 - 50}{4 - 2}=\frac{50}{2} = 25 \).

We can verify with another pair, say \((8, 200)\) and \((10, 250)\): \( m=\frac{250 - 200}{10 - 8}=\frac{50}{2}=25 \).

Step3: Write the equation

Since the slope \( m = 25 \) and the line passes through the origin (\( b = 0 \) in the slope - intercept form \( y=mx + b \)), the equation is \( y = 25x \).

Answer:

\( y = 25x \)