Exercise 45 Page 191

We want to write an equation in slope-intercept form that tells us the length of a sound barrier y in miles after x weeks. An equation in slope-intersect form has a value for the slope m and a value for the y-intercept b. y= mx+ b We need to find the values of m and b in the given context. We know that it takes the crew 1 week to build 12 of a mile. In our equation, y tells us how many miles the sound barrier is and x stands for the number of weeks. We can use the change in y and the change in x to find the slope. m=change iny/change inx=12/1= 1/2 This means that m= 12. The next step is to find the y-intercept. The y-intercept is the value of y when x equals zero. When x=0 it has been 0 weeks. At that time the sound barrier does not exist yet which means that y must be 0. Therefore, our value for b is 0. Let's substitute these values into our equation!

y= mx+ b

SubstituteII

m= 1/2, b= 0

y= 1/2x+ 0

IdPropAdd

Identity Property of Addition

y= 1/2x

We can visualize this in a graph. Remember that the total length of the sound barrier is 13 miles. This means that the y-value cannot be greater than 13.