the second problem, I needed to find a line that was perpendicular another
The given equation was y=-2x-4 and passed
through (1, 3). The ordered pair are
x1 = 1 and y1 = 3.
definition of perpendicular lines is that they must both have the reciprocal slope with opposite signs
and intersect each other in a coordinate plane.
comparing the given equation to the general formula y= mx + b, m= -2 is the slope and b= -4 is the y-intercept. To fine the perpendicular
line, based on the definition, I had to find the opposite reciprocal of -2 which 2. The new slope was 1/2 and the given point was (1, 3). I then used the
point-slope equation y-y1 = m (x – x1).
I substituted the new slope and ordered pair into the equation. The new
equation looked like this: y – 3 = 1/2 (x -1). I then used the distribution
property to alter the equation to look like this: y – 3= 1/2x -1/2. The last
step was to add 3 on both sides. The answer was y = ½ x + 5/2. But for the purpose
of graphing, I changed 5/2 to 2 ½. The final answer was y = ½ x+ 2 ½.
Mathematical steps below:
– y1 = m (x – x1)
– 3 = ½ (x – 1)
y – 3 = ½ x – 1/2
y = ½ x + 5/2
y = ½ x + 2 ½
For this problem, one line rises while the other
falls. Both lines then intersect each other. The y-intercept is 2 ½ above the origin
while the x-intercept is 5 units to
the left of the origin.