Question

I would appreciate the help!!

Answer 1

Answer:

a. $0.1\ miles$

b Slope: $\frac{1}{10}$ or $0.1$

Step-by-step explanation:

The equation of a line that passes through the origin is:

$y=mx$

Where "m" is the slope of the line.

By definition, Direct variation equations have the following form:

$y=kx$

Where "k" is the Constant of variation.

Then, you can conclude that:

$m=k$

a. Let be "d" the distance in miles that the train travels per gallon.

You can observe in the graph that when the train travels 10 miles, it uses 100 gallons. Then, you can set up the following proportion:

$\frac{10}{100}=\frac{x}{1}$

Solving for "x", you get:

$x=\frac{1}{10}\\\\x=0.1$

Then, it travels 0.1 miles per gallon.

b. The slope is also $\frac{1}{10}$ or $0.1$. To check this, you can subsitute the coordinates of the point (100,10) into $y=mx$ and solve for "m" in order to find its value.

This is:

$10=m(100)\\\\m=\frac{1}{10}$