Equations of Lines

1. The slope of a line through the points and is given by .

2. __Point-Slope Form__

The line through the point with slope m has the equation .

3. __Slope-Intercept Form__

The line with slope m and y-intercept b has equation .

4. Two lines with slopes and are

parallel iff

perpendicular iff .

**Ex 1 ** Find an equation of the line which passes through the point
and has slope 3.

**Sol** Using the Point-Slope Form, we obtain the equation
or,
simplifying, or .

If instead we use the Slope-Intercept Form, we get the equation . To determine b, we substitute and to obtain , so that .

**Ex 2 ** Find an equation of the line which passes through the point and
is parallel to the line .

**Sol ** To find the slope of the line , solve for y to get the equation
; so this line has slope . Since the line we are seeking
is parallel to this line, its slope is also , so its equation is
or or .

**Pr 1 ** Find an equation of the line which passes through the point and
has y-intercept 5.

**Pr 2 ** Find an equation of the line which passes through the points and
.

**Pr 3 ** Find an equation of the line which passes through the points and
.

**Pr 4 ** Find an equation of the line which passes through the point and
is perpendicular to the line .

**Pr 5 ** Find an equation of the perpendicular bisector of the line segment between
the points and .

**Pr 6 ** Find the slope-intercept form of the equation of the line which passes
through the point and which is parallel to the line through the
points and .

**Pr 7 ** Find an equation of the tangent line to the circle at the
point .

**Pr 8 ** Find the point of intersection of the lines with equations
and .

Go to Solutions.

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