equations of lines

Question

write the equation of a line passing through (-2,3) and:

a.) parallel to the line with equation x-2y=5 in slope intercept form.

b.) perpendicular to the line with equation x-2y=5 in standard form

Answer 1

slope intercept form is:

y=mx+b

 

where m is the slope

 

Start by rearranging the given equation to slope intercept form:

y=1/2x-5/2

 

for parallel lines, the slope is the same, so we can make a new equation, using the given point (-2, 3):

3=1/2(-2)+b

 

solve for b:

4=b

 

plug into new equation, taking out the given point for x and y:

y=1/2x-4

 

 

For perpendicular lines, the slopes are the negative opposites (aka reciprocals), so the new equation would be:

3=-2(-2)+b

 

making b now:

-1=b

 

so the perpendicular line equation in slope intercept form is:

y=-2x-1

 

But this question asks for standard form, which is Ax+By=C, so we need to convert it:

2x+y=-1