A line goes through point (-7,1) and is parallel to -3y+7x=12. Find a equation in point slope form and find equation in slope intercept form. Show your work
step 1
Find the slope of the given line
-3y+7x=12
isolate the variable y
3y=7x-12
y=(7/3)x-4
slope is m=7/3
step 2
Remember that
If two lines are parallell , then their slopes are equal
so
the slope of the parallel line is m=7/3
Find the equation in point slope form
y-y1=m(x-x1)
we have
m=7/3
point (-7,1)
substitute
y-1=(7/3)(x+7) -------> equation in point slope form
step 3
Find the equation in slope intercept form
y=mx+b
we have
m=7/3
point (-7,1)
substitute
1=(7/3)(-7)+b
1=-49/3+b
b=52/3
therefore
y=(7/3)x+52/3 ------> equation in slope intercept form
Problem N 2
A line goes through the point (3,-4) and is perpendicular to 5x+9y=1. Find an equation in point slope form and find equation in slope intercept form
step 1
Find the slope of the given line
5x+9y=1
9y=-5x+1
y=-(5/9)x+1/9
slope is m=-5/9
step 2
slope of the parallel line is m=-5/9
equation in point slope form is
y+4=-(5/9)(x-3)
step 3
equation in slope intercept form is
y=mx+b
m=-5/9
point (3.-4)
-4=-(5/9)(3)+b
-4=-(5/3)+b
b=-4+5/3
b=-7/3
therefore
y=-(5/9)x-7/3