A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.

 a=24

Step-by-step explanation:

Lets find the line's  formula (equation of the line).

As known the general formula of any straight line (linear function) is

y=kx+b

Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7

(Xb;Yb)- are the coordinates of point B

(Xa;Ya) are the coordinates of point A

Now lets find the coefficient b.  For this purpose we gonna use the coordinates of any point A or B.

We will use A

7=-2/7*3+b

7=-6/7+b

b=7 6/7

So the line' s  equation is y= -2/7*x+7 6/7

Now we gonna find the value of a usingcoordinates of point C.

Yc=1,  Xc=a

1=-2/7*a+7 6/7

2/7*a= 7 6/7-1

2/7*a=6 6/7

(2/7)*a=48/7

a=48/7: (2/7)

a=24

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: