Chapter 5.4, Problem 14P

Open-Ended Write an equation of a line that has a slope of $-\frac{1}{2}$ in each form.

a. point-slope form

b. slope-intercept form

To determine

To Write: The equation of the line in point-Slope form.

Answer to Problem 14P

Point slope form of a line is $y-3=-\frac{1}{2}(x-2)$

Explanation of Solution

Given information: The line has slope of $-\frac{1}{2}$

Formula used: The point-slope form of a line is $y-y_1=m(x-x_1)$ where m represents slope of the line.

Calculation:

For example let’s take a point (2,3) and for the given slope $-\frac{1}{2}$

Plug in the known values into the formula.

  $y-y_1=m(x-x_1)$

  $y-3=-\frac{1}{2}(x-2)$

Conclusion: One of the perpendicular lines in Point-Slope form is $y-3=-\frac{1}{2}(x-2)$

To determine

To Write: The Slope-intercept form of a line.

Answer to Problem 14P

The slope-intercept form of the line is $y=-\frac{1}{2}x+4$ .

Explanation of Solution

Given information: The slope of the line is $-\frac{1}{2}$ .

Formula used: The slope intercept form of a line is $y=mx+b$ where m represents slope and b represents y-intercept.

Calculation:

For example let’s use the same point that used for part A, (2,3).

Slope of the line is $-\frac{1}{2}$

Plug in the known values into the equation $y=mx+b$

  $y=-\frac{1}{2}x+b$

Substitute the point into the equation

  $3=-\frac{1}{2}(2)+b$

Simplify it

  $3=-1+b$

Add both sides 1.

  $b=4$

Plug in the b value into the equation

  $y=-\frac{1}{2}x+4$