Question

cassidy’s family is driving home from vacation at an average speed of 55 mph. after 2 hours they are 110 miles from home. what is an equation in point - slope form that represents their distance y from home, after x hours.
a ( y - 110 = - 55(x - 2) )
b ( y - 55 = 110(x - 2) )
c ( y - 2 = 55(x - 110) )
d ( y + 110 = 55(x + 2) )

Explanation:

Step1: Recall Point - Slope Form

The point - slope form of a linear equation is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.

Step2: Identify the Slope and the Point

• The speed of driving is 55 mph. Since they are driving towards home, the distance from home is decreasing over time. So the slope \(m=- 55\) (negative because the distance \(y\) from home is a decreasing function of time \(x\)).
• After \(x = 2\) hours, they are \(y = 110\) miles from home. So the point \((x_1,y_1)=(2,110)\).

Step3: Substitute into Point - Slope Form

Substitute \(x_1 = 2\), \(y_1=110\) and \(m=-55\) into the point - slope form \(y - y_1=m(x - x_1)\).
We get \(y - 110=-55(x - 2)\).

Answer:

A. \(y - 110=-55(x - 2)\)