Question

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?

Answer 1

Given:

Let time be the independent variable.

Let mile marker be the dependent variable.

On one highway, Gabriela noticed that they passed mile marker 123 at 1:00. She then saw that they reached mile marker 277 at 3:00 and Mr. Morales was driving at a constant speed.

The coordinates of the points on this line are (1,123) and (3,277)

We need to determine the slope of the line.

Slope of the line:

The slope of the line can be determined using the formula,

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

Substituting the points (1,123) and (3,277) in the above formula, we get;

$m=\frac{277-123}{3-2}$

$m=\frac{154}{1}$

$m=154$

Therefore, the value of the slope of this line is 154.