let
A (-5,-4) and B (5,10)
Part 1) write an equation for the line in point-slope form
we know that
the equation of a line in point-slope form is
y-y1=m*(x-x1)
step 1
find the slope m
m=(y2-y1)/(x2-x1)------> m=(10+4)/(5+5)----> m=14/10---> 7/5
strep 2
with m=7/5 and the point B (5,10)
find the equation of a line
y-y1=m*(x-x1)-----> y-10=(7/5)*(x-5)
the answer Part 1) is
y-10=(7/5)*(x-5)
Part 2) write an equation for the line in slope-intercept form
we know that
the equation of a line in slope-intercept form is
y=mx+b
step 1
find the slope m
m=(y2-y1)/(x2-x1)------> m=(10+4)/(5+5)----> m=14/10---> 7/5
step 2
with m=7/5 and the point B (5,10)
find b
y=mx+b
10=(7/5)*5+b-----> 10=7+b-------> b=3
the equation of the line is
y=(7/5)x+3
the answer Part 2) is
y=(7/5)x+3