Question

Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given the point to slope form is y +1 = 2/3 (x - 8)

Answer 1

we know that

the equation of the line in standard form is
Ax+By=C

the equation of the line in the slope-intercept form is
y +1 = 2/3 (x - 8)-----> y+1=(2/3)x-(16/3)----> y-(2/3)x=(-16/3)-1
y-(2/3)x=(-19/3)----> multiply by 3-----> -2x+3y=-19

the answer is
-2x+3y=-19

I verify that the points belong to the given line
for the point (8,-1)
-2*8+3*(-1)=-19--------> -16-3=-19-----> -19=-19------> is ok

for the point (2,-5)
-2*2+3*(-5)=-19------> -4-15=-19------> -19=-19-----> is ok