Chapter 5.6, Problem 6STP

A city designer is drawing the road map for a new housing development. Palm St. runs through the coordinates (11,5) and (-1,1) on the map. Pepperdine St. is going to run perpendicular to Palm St. The coordinates of Pepperdine St. are (4,7) and (7, y). What is the value of $y$?

What is the equation for the line representing Pepperdine St. in slope-intercept form?

To determine

To find: The value of y. The equation of the Pepperdine St. in Slope-intercept form.

Answer to Problem 6STP

  $y=-2$

Explanation of Solution

Given information: The coordinate of Palm St. runs through the coordinates (11,5) and (-1, 1). The Pepperdine St runs through the coordinates of (4,7) and (7,y). The Palm St and Pepperdine St. are perpendicular to each other.

Formula used: Use the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ ; the slope of perpendicular lines from any line is negative reciprocal.

Calculation:

Find slope of Palm St. using slope formula

  $m=\frac{1-5}{-1-11}$

Simplify it,

  $=\frac{-4}{-12}$

  $=\frac{1}{3}$

Now, using concept of perpendicular lines the slope of Pepperdine St is negative reciprocal of $\frac{1}{3}$ .

So, slope of Pepperdine St. $=-\frac{3}{1}$

Simplest form is -3.

Now, using slope formula find slope of Pepperdine St.

  $\frac{y-7}{7-4}=-3$

  $\frac{y-7}{3}=-3$

Multiply both sides by 3.

  $y-7=-9$

Add both 7,

  $y=-2$

Using equation $y=mx+b$

Plug in m as -3 and point into the equation to find the value for ‘ b’ .

And use the point (4,7).

  $7=-3(4)+b$

  $7=-12+b$

Add both sides 12.

  $b=19$

So, equation in slope-intercept form is $y=-3x+19$ .