Question

when driving on a highway, ian passed the 23 mile marker with 15 gallons of gas in the tank. when he passed the 73 mile marker, he had 12.5 gallons of gas left. question 1 part a if the number of gallons left in the tank is the dependent variable, find the slope of a graphed line that passes through these two points. what would the slope represent in terms of the context?

Answer 1

The slope of the graphed line that passes through the two points is -0.25 gallons per mile. In terms of the context, this represents the rate at which Ian is using up gas while driving.

Step-by-step explanation:

To find the slope of a graphed line passing through the two points, we use the formula:

slope = (y2 - y1) / (x2 - x1)

Using the given information, the first point is (23, 15) and the second point is (73, 12.5). Plugging these values into the formula, we get:

slope = (12.5 - 15) / (73 - 23) = -0.25 gallons per mile

In terms of the context, the slope represents the rate at which Ian is using up gas while driving. Each mile he travels, he uses up 0.25 gallons of gas.

Answer 2

Part A The slope is -0.05 gallons/miles

Part B The slope is the rate at which the vehicle consumes fuel in gallons per mile

Part A if the number of gallons left in the tank is the dependent variable, find the slope of a graphed line that passes through these two points.

To find the slope bewteen the two points, we use the equation for sllope between two points (x₁, y₁) and (x₂, y₂)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Given that the points

• (x₁, y₁) = (23 miles, 15 gallons) and

• (x₂, y₂) = (73 miles, 12.5 gallons) (since the gallons in the tank are the dependent variable

Substituting these into the equation, we have that

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

what would the slope represent in terms of the context?

m = (12.5 - 15) gallons/(73 - 23) miles

m = -2.5 gallons/50 miles

m = -0.05 gallons/miles

So, the slope is -0.05 gallons/miles

Part B. what would the slope represent in terms of the context?

Since the slope is -0.05 gallons/miles, this is the rate at which the vehicle consumes fuel in gallons per mile