ANSWER
a=-32
EXPLANATION
If C(a,1) is on the line that passes through A(3, 7), and B(-4, 9), then the three points are collinear.
This implies that, when we find the slope using any two points, we should get the same result.
[tex] \frac{9 - 1}{ - 4 - a} = \frac{9 - 7}{ - 4 - 3} [/tex]
We simplify to obtain;
[tex] \frac{8}{ - 4 - a} = \frac{ - 2}{ - 7 } [/tex]
[tex]\frac{8}{ - 4 - a} = \frac{ 2}{ 7 } [/tex]
We cross multiply to get;
[tex]8 \times 7 = 2( - 4 - a)[/tex]
This implies that,
[tex]56 = - 8 - 2a[/tex]
[tex]56 + 8= - 2a[/tex]
[tex]64 = - 2a[/tex]
Divide both sides by -2
[tex]a = \frac{64}{ - 2} [/tex]
[tex]a = - 32[/tex]
