Question

Help please

Which equations in point-slope form are equations of the line that passes through the point (−7, 5) and (−4, 1)?

Choose exactly two answers that are correct.

A.y-7= -3/4(x+5)


B.y-5= -4/3(x+7)


C.y+4= -3/4(x+1)


D.y-1= -4/3(x+4)

Answer 1

an easy way to do it is subtituet (-7,5) and (-4,1) into the equations and find out which ones check. remember (x,y)

so A
if we try (-7,5)
5-7=-3/4(-7+5)
we can immediately see that -2 is not equal to -3/4(-2)
so A is wrong


B
if we try (-7,5)
5-5=-4/3(-7+7)
0=-4/3(0)
0=0
so B is correct

C
if we try (-7,5)
5+4=-3/4(-7+1)
9=-3/4(-6)
9 is not equal to 18/4
so C is wrong

D
if we try (-7,5)
5-1=-4/3(-7+4)
4=-4/3(-3)
4=12/3
4=4
D is correct

If you wanted to try the second point (-4,1) in B and D
B
1-5=-4/3(-4+7)
-4=-4/3(3)
-4=-12/3
4=4
B is still correct

D
1-1=-4/3(-4+4)
0=-4/3(0)
0=0
D is still correct

so the answers are B and D

Answer 2

`General\ equation\ for\ line\ in\ slope\ intercept\ form:\\\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (-7,5)\ (-4,1)\ into\ equation\\\\ \left \{ {{5=-7a+b}\ \ \ \ \atop *-1} \right.\\\\ \left \{ {{5=-7a+b}\ \ \ \ \atop {-1=4a-b}} \right.\\\\ +----\\\\Addition\ method\\\\ 4=-3a\ \ |:(-3)\\\\ a=-(4)/(3)\\\\ b=5+7a=5+7*(-(4)/(3))=5-(28)/(3)=-4(1)/(3)\\\ Answer\ y=-(4)/(3)x-4(1)/(3)\\\\ Checking\ solution:\\ y-5=-(4)/(3)(x+7)`
`y-5=-(4)/(3)x-(28)/(3)\\\\ y=-(4)/(3)x-(28)/(3)+5\\\\ y=-(4)/(3)x-4(1)/(3)\\\\Answer:B \ and\ D.`