Question

During the trip, the Morales family drove on several different highways. Gabriela and Luis noticed that sometimes the mile markers were increasing, and other times the mile markers were decreasing.



On one highway, Gabriela noticed that they passed mile marker 123 at 1:00. She then saw that they reached mile marker 277at 3:00. Since Mr. Morales was driving at a constant speed, their mile-marker location over time can be represented by a line where the time in hours is the independent variable and the mile marker is the dependent variable. The points (1,123) and (3,277) are two points on this line.

What is the value of the slope of this line?

Enter your answer as the correct value, like this: 42

If your answer is a fraction, use the / symbol. For example, if your answer is 314, enter your answer like this: 3/14

Answer 1

Answer:

The slope of the line is 77

Explanation:

We know the speed is constant and that the mile-marker location over time can be represented by a line. This means that the equation is linear.

The slope can, therefore, be calculated as follows:

$slope = \frac{y_2-y_1}{x_2-x_1}$

where (x₁ , y₁) and (x₂ , y₂) are two points on the line

We are given that the two points (1, 123) and (3, 277) are two points in the line

Substitute with them in the above equation to get the slope as follows:

$slope = \frac{277-123}{3-2}=77$

Hope this helps :)