Question 720045
The slope of the line y = (2/7)x+1 is 2/7. The slope of any perpendicular line will be the negative reciprocal of the the slope of this line. So the slope of our perpendicular line will be -7/2.<br>
The slope of the line through (k, -7) and (6, 6) will be (according to the slope formula):
{{{(6-(-7))/(6-k)}}}
or
{{{13/(6-k)}}}<br>
We want the line through (k, -7) and (6, 6) to be perpendicular to y = (2/7)x+1. So its slope needs to be -7/2. Therefore:
{{{13/(6-k) = -7/2}}}<br>
Now we solve for k. Cross-multiplying we get:
{{{13*2 = (6-k)*(-7)}}}
Simplifying:
{{{26 = -42 + 7k}}}
Adding 42:
{{{68 = 7k}}}
Dividing by 7:
{{{68/7 = k}}}