Lines in the Plane and Slopes

  1. Slope: MATH

  2. Equation of a line:

  3. Slope Intercept Formula: $y=mx+b$

  4. Point Slope Formula: $y-y_1=m(x_2-x_1)$

  5. Vertical Line: $x=a.$

  6. Horizontal Line: $y=b$

  7. Parallel lines: If $l_1$ is parallel to $l_2,$ then $m_{l_1}=m_{l_2}$

  8. Perpendicular lines: If $l_{1}$ is perpendicular to $l_{2},$then MATH

Exercises:

Given $P=(0,3),$ and $Q=(-4,5),$ then

(a) find the line equation passes through $PQ,$

(b) find the line equation of $l_1$ so that $l_1$ passes through $P$ and $l_1 $ is perpendicular to $PQ,$

(c) find the line equation of $l_2$ so that $l_2$ passes through $Q$ and $l_2 $ is parallel to $l_1,$

(d) find the midpoint of $P$ and $Q,$

(e) find the standard equation of the circle which uses $PQ$ as its diameter.

Repeat the problem above by using the following pair points $P$ and $Q.$

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