Q2 Q13.) Use the given conditions to write an equation for the line in​ point-slope form and​ slope-intercept form.

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