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 .