Chapter ISG, Problem 4.1STP

To determine

To calculate the equation of line.

Answer to Problem 4.1STP

The equation of line in slope y-intercept form is, $y=\frac{-1}{2}x+3$

The equation on line in point slope form is $y+1=\frac{-1}{2}(x-8)$

Explanation of Solution

Given information:

The line1 passes through (8, -1)

The line2 is perpendicular to, $y=2x-9$

Formula used:Product of slopes of 2 perpendicular lines is -1

Equation of line is,

  $y=mx+c$

Equation of line in point slope form,

  $(y-y1)=m(x-x1)$

Calculation:

Comparing the given equation of line2 to the equation of line,

Slope of the line is 2

Since, product of slopes of two perpendicular line is -1, therefore, slope of line1 is,

  $2\times m=-1$

On solving,

  $m=\frac{-1}{2}$

Hence, slope of line1 is $\frac{-1}{2}$

Substituting the values of line1 in the equation of line,

  $y-(-1)=\frac{-1}{2}(x-8)$

On solving,

  $y+1=\frac{-1}{2}(x-8)$

Hence, the equation on line in point slope form is $y+1=\frac{-1}{2}(x-8)$

On solving the point slope equation,

  $y+1=(\frac{-1}{2}x)-(\frac{-1}{2}\times 8)$

So,

  $y+1=\frac{-1}{2}x+4$

Shifting left- hand side variables to right-hand side,

  $y=\frac{-1}{2}x+4-1$

On solving,

  $y=\frac{-1}{2}x+3$

Hence, the equation of line in slope y-intercept form is, $y=\frac{-1}{2}x+3$