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Anonymous

For the second problem, I needed to find a line that was perpendicular another given equation.

The given equation was y=-2x-4 and passed
through (1, 3). The **ordered pair** are
x_{1} = 1 and y_{1} = 3.

The
definition of perpendicular lines is that they must both have the **reciprocal** slope with opposite signs
and intersect each other in a coordinate plane.

Again
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-y_{1} = m (x – x_{1}).

First,
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:*

y
– y_{1} = m (x – x_{1})

y – 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**.

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