Question

Consider the following.
Point
(-5, 4)
 Line   
x + y = 7
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.

Answer 1

x + y = 7....y = -x + 7....the slope here is -1

A. a parallel line will have the same slope
    y = mx + b
    slope(m) = -1
    (-5,4)...x = -5 and y = 4
    sub and find b, the y int
    4 = -1(-5) + b
    4 = 5 + b
    4 - 5 = b
    -1 = b
so ur parallel line is : y = -x - 1 <==

B. perpendicular lines have negative reciprocal slopes. That means our perpendicular line will have a slope of 1
   y = mx + b
   slope(m) = 1
   (-5,4)...x = -5 and y = 4
   now we sub and find b, the y int
   4 = 1(-5) + b
   4 = -5 + b
   4 + 5 = b
   9 = b
so ur perpendicular line is : y = x + 9 <==