Two points determine a line. The problem gives point A(3,7) and point B(-4,9). It also says that point C(a,1) is on the line.
Now, 'a' is the value of x when y=1. That is, C(a,1) is on the line, so x=a and y=1. We can determine the value of 'a' by first determining the equation of the line.
y-y1 = ( (y2-y1) / (x2-x1) ) (x - x1)
y-7 = ( (9-7)) / ((-4)-3) ) (x - 3)
y-7 = (-2/7)x + 6/7
y = (-2/7)x + 55/7
Now, solve for x (that is, a) when y=1.
1 = (-2/7)a + 55/7
(2/7)a = 48/7
2a = 48
a = 24
The value of 'a' is 24. The point (24,1) is on the line.
Is 1 = (-2/7)(24) + 55/7 ?
7 = -48 + 55 ?
7 = 7 ?yes
Since you mentioned 'graphing linear equations,' when you plot the line, the point C(24,1) should be on the line.