Writing Equations of Lines

To write the equation of a line you MUST have the slope and a point.

 Suppose the slope is given as m=5/12 and the given point is (-3, -9).  You are asked to “Write the equation of the line with the given slope and that passes through the given point in STANDARD FORM.”

 You may ALWAYS start with the point-slope formula.  In general, the maximum number of steps that you might do is 8.  Some of the problems will involve fewer steps.

If the question had been “Write the equation of the line with the given slope and that passes through the given point in SLOPE INTERCEPT FORM,”  the process would have been the same through Step  6.  From there the solution would follow this pattern.

There are numerous ways to “give” the slope and point in the question statement.  Here are some of the ways that our current textbook does so:

EASIEST QUESTIONS:

 1.  Find an equation with slope –4/5 and y-intercept (0, -2)……….pretty straightforward, and you have a special point (the y-intercept), so you can start with y=mx+b!

 2.  Find an equation of the line satisfying the condition m=5, b=15…..hum, pretty easy, just like above!

 3.  Find an equation of the line shown in a graph…hint: use any two points to find the slope by counting, and then you have the slope, and a point  (use point-slope).

 4.  Find an equation of a line through (-3,6) that has a slope of –4……(use point-slope).

 A LITTLE MORE THOUGHT PROVOKING QUESTIONS:

 5.  Find an equation of the line that passes through (-4, -3) and (5, 9).  Here you must use the points to first FIND the slope; then use the slope and one of the points…(use slope formula, followed by point-slope form).

 6.  Find the equation of the line through (7, 2) parallel to 3x-y=8.  Here you must get the slope of the line (it is 3, why?).  Since parallel lines have the same slope, the equation you will write has a slope of 3 and passes through (7, 2)…makes the problem like #4.

 7.  Find the equation of the line through (7,2) perpendicular to 3x-y=8.  Here, once again you must get the slope of the line (m=3).  Since perpendicular lines have slopes that are negative reciprocals, the equation you will write has a slope of m=-1/3 (why?)  and passes through (7,2)…makes the problem line #4.